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The Sweden international's contract with the French champions expires at the end of next season and he has endured a difficult few weeks after a foul-mouthed rant was caught on camera earlier this month.
The often controversial Ibrahimovic appeared to criticise the match referee following a defeat to Bordeaux, claiming France "don't even deserve PSG to be in this country".
Ibrahimovic was also sent off in the second leg of PSG's UEFA Champions League progression against Chelsea but former goalkeeper Schmeichel has called on United to do everything they can to sign the forward.
"Last summer there were rumours that he would come to Manchester United. I said then that Zlatan was built for the club, he was born to play there," the Dane told L'Equipe.
"It's why [Eric] Cantona was so strong when he was there, not at Leeds [United] or in all other clubs in France? Why? Because it is Manchester United.
"In Manchester, there was the freedom given to the players, but also responsibilities.
"We do not care who you are or what you love, we look at what you're doing on the pitch and the influence you have in the club. If you do not respect that, you're leaving.
"But you can have any personality. [David] Beckham, Cantona, they could go out and also be at their best. There are hundreds of players who are trying to be a Beckham or Cantona, but do not have the personality, and they fail."
