The Swede has been in stunning form for the club since his arrival from Paris Saint-Germain on a free transfer in the summer.
Ibrahimovic has struck 19 goals in 29 appearances this season and has been widely praised by teammates for his impact on and off the field.
United have an option to extend the 35-year-old's current contract, which expires in the summer, for another 12 months.
But, according to a report in The Sun, Jose Mourinho wants Ibrahimovic stay for two more years.
The veteran forward recently likened himself to a red wine, claiming he is getting better with age and could play on until he's 50.