Celtic club chiefs reportedly flew to Mallorca over the weekend to hold face-to-face talks with Brendan Rodgers.
It's claimed chief executive Michael Nicholson and finance director Chris McKay flew by private jet to Rodgers' home in Spain on Saturday to discuss a return to Parkhead.
The former Leicester boss has been a frontrunner for the job since Ange Postecoglou's exit for Tottenham Hotspur last week.
However, doubts emerged with Rodgers having planned time out from football after being dismissed by Leicester last season.
The Daily Mail report, though, that Rodgers has held initial talks with Celtic chiefs over a possible stunning return to Glasgow.
It's thought Rodgers has the backing of Celtic supremo Dermot Desmond and will consider an opportunity to return to the club ahead of fresh discussions this week.
And Celtic could convince John Kennedy to remain in Glasgow with the return of Rodgers, it's reported.
Postecoglou is keen to bring Kennedy - as well as Gavin Strachan and analyst Greg Wallace - to Spurs but Celtic are intent of retaining the services of the coach.
And the report suggests Rodgers returning to Celtic could keep Kennedy with Chris Davies in the running for the Swansea job.
Speaking previously on a possible return to Parkhead in the future, Rodgers said: "The club were keen to bring me in and they were in a moment where Rangers were close - they were getting promoted - and I went in and created hopefully a really good base.
"That challenge may come again because it was a real challenge to go in and that challenge may come in the future and I would have absolutely no hesitation going back.
"Incredible club but like everything in life it's just about timing.
"Whether I would be received back or not is a different story.
"But would I go back to Celtic? Absolutely."
