Ibrahimovic moved to Old Trafford as a free agent last summer and has scored 26 goals already for the Red Devils.
The Swedish striker scored twice at Wembley on Sunday, as United overcame a resilient Southampton team 3-2 to win their first trophy of the season.
The 35-year-old signed a one-year deal with an option for a further 12 months, but that clause has not been activated yet.
Speaking after the EFL Cup final, Mourinho said: “I never beg for players to sign. But if need be, Manchester United fans can go to his house and stay all night.”
There are doubts Ibrahimovic may extend his stay in England, if United don’t qualify for the Champions League next season.