The Blues are ready to offer him a lucrative deal when his contract ends in 2021.
The speculations have been doing rounds as Barcelona ended their UCL season with their worst-ever defeat (2-8).
Barcelona lost out on La Liga 2019-20 title after a spell of inconsistency.
The Spanish club had won the 2017-18 and 2018-19 editions but failed to script a hat-trick, this time around.
Notably, Real Madrid emerged champions this season to snatch the honor from their arch-rivals.
Barcelona's Champions League defeat to Bayern Munich further rubbed salt into the wounds.
Barcelona President Josep Maria Bartomeu has called a crisis meeting wherein he is likely to sack current manager Quique Setien.
Meanwhile, sporting director Eric Abidal will also be under the scanner.
Reportedly, former Tottenham boss Mauricio Pochettino is a front-runner to replace Setien.
The Argentine stands atop along with former Barcelona aces Xavi and Ronald Koeman for the spot.
As the La Liga season concluded, Messi highlighted the club's inconsistent run.
"We didn't expect to finish in this way, but it sums up the year for us. We are a weak team who can be beaten with enough intensity and enthusiasm," Messi said to reporters.
"We have lost a lot of points which we shouldn't have done. We have been very inconsistent."
During the season, Messi became the only player to score over 20 goals in 12 consecutive La Liga seasons.
He also registered his 700th career goal as Barcelona and Atletico Madrid played out a 2-2 draw in gameweek 33.
Eventually, he became the first ever player in La Liga history to claim a double of 20 goals and 20 assists (in a single season).
It is understood that Manchester City are planning to reunite boss Pep Guardiola and Messi.
This could help Messi secure a few more trophies before he calls it quits.
As history states, Guardiola knows how to get the best out of the latter.
Although Messi's current buy-out clause is a whopping £635 million, Barcelona's financial state could see them settle for much less.
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