The 25-year-old joined United from Norwegian side Molde in 2009 and memorably scored on his home debut in a 3-0 win over Burnley.
However, he has since failed to establish himself at Old Trafford, and scored just six goals in 29 games while on loan to Blackburn for the whole of last season.
And it now appears he could soon be on his way out of the club, after Hannover sporting director Jorg Scmadtke revealed United have accepted their bid for Diouf.
"We have an agreement with Manchester United," Schmadtke told Sky Germany. "Now, the player must give us his okay."
Diouf has only made three appearances for the Red Devils this season, with all of them coming in the Carling Cup.