The two worked together while at Inter Milan during the 2008/09 season and have both been linked with a move to Old Trafford in recent weeks.
Speculation linking the Portuguese tactician with the Red Devils has intensified in recent weeks, with a poor campaign continuing to build pressure on current boss Louis van Gaal.
A 1-0 win over Aston Villa on Saturday leaves United sitting four points behind Arsenal in the race for the final Champions League spot, with the club's board reportedly close to losing patience with the Dutchman.
According to Bild, Mourinho is poised to sign a three-year deal at Old Trafford, adding that Ibrahimovic will join him in Manchester, with a move away from French champions Paris St-Germain looking increasingly likely.
However, a potential stumbling block is whether the 34-year-old would be willing to join United should they fail to reach the Champions League.