The Spaniard secured his best result of the season in the Monaco Grand Prix as he took second place behind Verstappen in the rain-affected race.
But although his fifth podium finish of the year has confirmed Alonso's spot as Red Bull's main challenger, he has already slipped to 51 points adrift of Verstappen in the drivers' standings.
The current advantage that Red Bull has over the rest of the field means there is little hope of Alonso being able to take the challenge to Verstappen in pure pace terms, but that has not left the double world champion thinking there is no hope of the title this year.
Alonso thinks that seasons like he had with Ferrari in 2010 and 2012 – where he was in contention for the championship until the final round despite not having the best car – have shown exactly what is possible over the course of a campaign.
Asked after the Monaco GP about his thoughts on the title, Alonso said: "Let's see. I think in any other of the seasons that I remember, back in the 2000s or early 2010s, I would be leading the championship with the results that I got this year.
"But now there is Red Bull and Max dominating every race. Even with great results, you're just stepping behind them, every race. So, I don't know.
"But we didn't have the best car in 2010 and we arrived leading the championship in Abu Dhabi. We didn't have the best car in '12 and we still fight for the championship until the last lap in Brazil. So, the championship is long, and we will not give up.
"We will need weekends where Red Bull has some issues, like Sergio [Perez] had here [in Monaco] with the DNF or zero points. And if Max has one or two of those, we will be a little bit closer in the championship. This is motorsport. Anything can happen. But on pure pace. I think we don't have the chance yet. But we will not give up for sure."
Alonso raised some eyebrows at the end of the Monaco GP podium celebrations when he deliberately put one of his feet on the race winner's step, in a move that some thought was to send a message about his victory aspirations.
But Alonso played down those suggestions, as he said he was not consumed by thoughts of getting what would be his first win in F1 for a decade.
"I will always take a picture on position one at the end after the champagne," said Alonso. "So yeah, I touched it a few times already this year.
"I will love to receive the trophy from there but yeah, I'm not getting obsessed with this to be honest. I will be happy fighting for the championship with all second places until the end of the year or fighting for the championship next year. This year is just a gift.
"What we are having every weekend is just a celebration with the team. We didn't expect this and this is just a build-up into next year, so hopefully good things are coming."
