The veteran Swedish striker, 34, signed a one year deal with an option for a further season this summer.
But Mourinho thinks he already so happy in England that he will stay for the extra year when he will be nearly 36.
GETTY
Jose Mourinho confident Zlatan Ibrahimovic will stay at Manchester United for two years
“I have no doubts he will be here for the next two years,” said Mourinho.
“I see him happy. I ask him every day. I know how important it is for him, because he is a family guy, for his wife, kids, house, everybody around him to be happy - and they are. His motivation is really high. “
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Ibrahimovic has made an immediate impact following his free transfer move from Paris Saint-Germain, scoring a goal in each of his three appearances so far.
The first against Galatasaray in a pre-season friendly, then in the Community Shield against Leicester and another on his Premier League debut at Bournemouth.