Mourinho wants to add two more players to his squad with a second bid for Borussia Dortmund's Henrik Mkhitaryan under serious consideration.
United have offered an improved bid believed to be around £26m for the 27-year-old playmaker, and are awaiting an answer from the German club.
Speaking about their Armenian No 10, Dortmund CEO Hans-Joachim Watzke admitted that they were considering an improved offer from Manchester.
Former United midfielder Paul Pogba is also on Mourinho's radar, although whether the club can force Juventus to sell the dynamic Frenchman remains to be seen.
Ibrahimovic plundered 38 goals for PSG as they cruised to the Ligue 1 title. That success saw the targetman pick up his 13th league championship in the last 15 seasons.
Ibrahmiovic is yet to play in England but has tasted success in Holland, Spain, Italy and France, although he failed to score at Euro 2016 before announcing his international career had come to an end.
While the deal could go through as early as Friday, United may delay announcing it until next week.
On Tuesday, Mourinho is set to be unveiled by the club to the world's media.