City are understood to be working out whether they can afford to sign him under current Financial Fair Play rules.
The Argentine has informed the club of his desire to leave Camp Nou, thought to be down to a combination of his own disillusionment and Barca's forensic appraisal of their recent failings.
The club's embarrassing 8-2 thrashing by Bayern Munich in the quarter-finals of the Champions League meant they ended a campaign trophy-less for the first time since 2013/14.
But they have been declining for a number of years, with that defeat their fourth last-eight exit in five seasons and issues off the field with presidential elections looming.
Quique Setien was almost immediately sacked as head coach, with club legend Ronald Koeman leaving his position as Netherlands boss to take charge.
While the Dutchman has, unsurprisingly, spoken in glowing terms when it comes to Messi, expressing a strong desire to build his team around him, that may not be possible as new sporting director Ramon Planes looks to revive Barca's fortunes.
Publicly, Barcelona claim Messi will only be sold should his €700m release clause be met, but there is that infamous clause in his contract that allows him to walk away for free.
The Argentine is now 33-years-old with officially only a year left on his £500,000 per week contract, and there's already talk of legal challenges on whether that clause is or isn't able to be used this summer.
Can Barca really risk him leaving for nothing, and how much rebuilding could be done if he was sold?
That will be what Planes has to weigh up.
Real Madrid cashed in on a Cristiano Ronaldo of the same age in 2018 when Juventus offered them €100m, and a similar situation could well be on the cards here.
While Messi has remained heavy odds-on to stay in Catalonia, City have recently moved into that position and he's now favoured to sign for Pep Guardiola ahead of staying at Camp Nou.
Messi has spoken on numerous occasions about wanting to play under his mentor again before he hangs up his boots, and this could be his last chance to do that.
Can City afford him though?
They have already spent just shy of £70m on Nathan Ake and Ferran Torres this summer and are close to completing a £60m deal for Kalidou Koulibaly, all of which is partly offset by the £40m sale of Leroy Sane to Bayern.
But any deal for Messi that would cost a minimum of £100m in transfer fees, plus his £25m annual salary, is a staggering outlay, even for the a player of his ilk.
City obviously think it's both a possibility and worth considering however, otherwise they wouldn't be looking into how they can balance their books to make it work.
The latest rumours may not be music to the ears of City's Premier League rivals, but for both City and neutral fans, why not get excited? Imagine the prospect of the greatest player of all time plying his trade on these shores.
Throughout Messi's time at the top, there have been potent front threes that the media have loved to make an acronym out of: BBC (Benzema, Bale, Cristiano), MSN (Messi, Suraez, Neymar) and even for one incredible season, SSS (Sterling, Suarez, Sturridge).
An SAM of Raheem Sterling, Sergio Aguero and Lionel Messi really does whet the appetite.
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