The Argentine handed in a transfer request last week after almost two decades at Camp Nou, winning 10 La Liga titles and four Champions League trophies.
Barca have been on a downward slope for years and their humiliating 8-2 loss to Bayern Munich in the Champions League reinforced how far they have fallen.
Messi opted not to turn to up to training on Monday as he is said to no longer consider himself a player of the club.
A move away from Barcelona won’t be straightforward, as the Catalan club are demanding that any potential suitors will have to pay his £632millon release clause, a stance that has been backed by La Liga.
There have been suggestions that the 33-year-old could change his mind should current president Josep Maria Bartomeu resign.
However, Freixa, who is vying to take Bartomeu’s place, says Messi’s decision to leave is irreversible and a move to Man City looks ‘likely’.
‘As I have heard from several sides, the decision the player has come to is one that has matured over several years and is irrevocable. I don’t believe that there is any going back,’ Freixa told Goal.
‘Messi is a player who strives for maximum success. He alone cannot achieve maximum success, he needs a team for that. He does not have one. Since the treble in 2015, Champions League success is missing.
‘That is what concerns him. His decision is due to the negative sporting development of the team in recent years.’
‘I think a move to Man City is likely,’ Freixa added.
‘With Pep, Messi experienced his most brilliant years in Barcelona. It would only be logical if both of them worked together again.
‘City, like almost all English clubs, also has the financial means to build a team that can win anything.’