Hannover, who beat Nuremberg 1-0 on Friday to remain in seventh place in the Bundesliga, are also in contention in the Europa League.
"I am happy that with Mame Diouf we have another alternative up front," said Hanover coach Mirko Slomka. "We need to bring him in fast so he can help us in the Bundesliga and the Europa League."
Senegal international Diouf joined United from Norwegian side Molde in 2009 and spent the 2010/11 season on loan at Blackburn Rovers.
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