Take your pick of any number of top players around Europe and you can bet that they have been linked with Liverpool at some stage over the past couple of years.
A club the stature of Liverpool means that Anfield will always be mooted as a potential destination for Europe's best and brightest, despite the measured inclinations of the owners towards spending. A Champions League crown and Premier League title in the past three years, not to mention the lure of working under one of the world's greatest coaches in Jurgen Klopp point to an enticing proposition.
But there have been names linked more than others, some that make a lot more sense both in football and financial terms.
Ousmane Dembele has been one of those names.
A player who had a £135m fee paid for his services by Barcelona as a 20-year-old in 2017 in a deal that had a buyout clause of £330m, is now linked once more as his time with the Catalan giants, one that has been beset by injury problems, has taken another ugly turn.
French international Dembele has been told he can leave Barcelona, with director Mateu Alemany stating: "We understand Dembele's decision not to continue, and we also informed him of our decision, we want committed players. Dembele has to leave as soon as possible and we've told him that.
"We told Dembele he has to leave immediately. We expect Ousmane to be sold before January 31."
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That comes after Dembele's agent, Moussa Sissoko, had made public a bitter row between club and player over the way Barcelona had sought to expedite the process of Dembele penning a new contract on reduced terms with the La Liga giants, who have been severely impacted financially during the pandemic.
Sissoko told RMC Sport in France: "They're putting the pressure on, but it doesn't work with people like us. Maybe it works with agents who are close to Barcelona. That's not the case with me, I'm here to defend my player's interests.
"We're not here to react to debates on social media, but the truth has to be said. Yes, we have high demands, but we've shown in the past that Ousmane's career choices are not dictated by money, else he wouldn't be here."
Dembele is out of contract in the summer and there will be undoubtedly be plenty of suitors for a player who cost £135m in 2017 and is still yet to celebrate his 25th birthday.
Barcelona, however, will want to try and cash in now on what has turned out to be another financial disaster similar to the one that they suffered with Philippe Coutinho when they spent £142m to lure him from Liverpool in 2018.
Dembele's return of 18 goals in 87 games wasn't what they were expecting.
But maybe the problem isn't that Coutinho and Dembele simply couldn't live up to their billing, more a club like Barcelona, who were feeling around in the dark for their former glories that Pep Guardiola delivered in the late 2000s and early 2010s were a side so disjointed, lacking in a solid transfer structure and simply throwing big numbers around in the hope that an assemblage of costly talent would somehow deliver past glories. Change at the top doesn't help either, with Dembele now playing under his fifth manager.
Coutinho's name had been floated for a potential return to Anfield, but a player approaching 30 and whose peak has likely passed, who also would command a fairly weighty fee in excess of £30m after any loan deal, was never likely to pass the sniff test for Liverpool's recruitment team, nor Fenway Sports Group's desire for financial responsibility.
Aston Villa took that particular plunge.
Dembele is different.
Dembele was schooled in the Borussia Dortmund way, much like Jude Bellingham is being now, albeit Dembele's arrival at Signal Iduna Park came a year after Klopp left Germany for Liverpool in 2015.
He is a player who Klopp is understood to have been an admirer of previously.
His time at Barcelona has been a struggle and a transfer market value that once was as high as £135m has now fallen, according to analysts at KPMG, to around £30m.
Some of that is attached to his contract being up in the summer, but the decline in value has been a steep one over the past 18 months or so, not aided by Barcelona's own financial position and weakened negotiating hand.
Analysts at the CIES Football Observatory in Switzerland, a group that analyses a number of factors when determining value, place him at around £16m.
Of course, wage demands would be where any kind of real cost would be incurred, with Dembele reportedly seeking as much as £30m per year, with the Daily Mail also suggesting representative fees and a signing on bonus to take that figure to almost double that.
That is likely a negotiating tactic, with Dembele understood to be less than pleased with the arrival of Ferran Torres from Manchester City, concerned that Barcelona wanted to negotiate a new deal in order to be able to sell him for a fee and recoup some of their major outlay on him this coming summer.
Realistically, Dembele will know nobody will be paying anywhere near that.
And with Liverpool and Mohamed Salah still not having reached an agreement over his new deal, one that would be far, far less than the sums Dembele was reportedly seeking to remain at Barcelona, any figures such as those being presented would be balked at.
Dembele is earning around the £200,000 per week mark at present at Barcelona, and given his time at Barcelona has been less than glittering, retaining the status quo would be seen as a success for a player who has been offered reduced terms to remain at the Nou Camp.
If Dembele's demands came back into reality from the far reaches of outer space that they reportedly find themselves in at present, a £200,000 per week striking addition operating at an elite level is pretty much par for the course nowadays. Low, in fact.
But if the Frenchman held firm in believing his value to be above the market price then it may not be the bargain it seems on the surface, especially with Liverpool's wage bill already rising at a faster rate than revenue growth.
Should wages make sense then you feel this kind of deal would be one that Liverpool and FSG would look at with some intrigue.
The Reds would acquire a player who fits their age bracket, who has been unable to deliver his best elsewhere and has been undervalued by management, as well as someone who has the potential to see his value soar and offer a financial incentive should it not work out as hoped.
Open season will be had on Dembele when a free agent, with competition likely fierce.
It would also raise the wages he would likely be seeking.
Paying a fee and getting things done early can pay off in shaving off some money from wage demands.
Until the future of Liverpool's crown jewel in Salah is resolved, though, it's hard to pre-empt where FSG's head will be financially heading into this summer.