PSG is currently looking for players who have higher talent after Mbappe left because PSG is worried that when Mbappe leaves him his performance will definitely decline so PSG is trying to bring in Julian Alvarez even though I think this will be very impossible.
Coming back to Manchester City, if they are tempted by the big offer from PSG and won't have a problem with Julian Alvarez leaving, that could happen but the only question is whether Julian Alvarez wants to risk his career with PSG who will forever be the rulers of League 1 without being able to win a title better.
PSG can offer Julian Alvarez a big salary but the problem is what about his future career? Julian Alvarez is a talented young player playing in one of the most competitive leagues in the world. If Julian Alvarez chooses to move to PSG then he will be able to win the Ligue 1 title but I am afraid his career will decline. Not many people watch Ligue 1 compared to the EPL. This is the same as what happened to Donnarumma, whose career is no longer in the spotlight because he chose to play in the farmers' league.
Actually joining PSG is not as bad as we imagine, indeed Ligue 1 is not as attractive as the Premier League, but I don't think Alvarez career will fade when he joins PSG. Financially, PSG will have no difficulty paying for Alvarez release clause from City, and PSG is also very capable of paying him a high salary.
PSG is actually not alone in hunting for Alvarez signature, where Chelsea and ATM are also very interested in the player from Argentina. Alvarez needs a team that can provide regular playing time, because at City Alvarez is always the second choice after Halaand. It seems that Alvarez is more likely to join Chelsea than PSG or ATM.
If Alvarez chooses PSG, it is clear he will be the main choice without significant competition and Enrique needs a replacement for Mbappe, while at Chelsea Alvarez will compete with Jackson and Nkunku to ensure the main place. Apart from that, if he joins PSG, Alvarez can still win trophies every season, and still play in the Champions League every season, in this case Chelsea cannot do that.