The Scot left Old Trafford on Tuesday after just 10 months in charge of the Red Devils, with the club set for their lowest Premier League finish since 1989-90.
Benitez has previous Premier League experience, most recently with Chelsea, but also spent six years at United’s bitter rivals, Liverpool, winning the Champions League with the Reds.
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"It is certainly a name they should consider," he told talkSPORT. "They need somebody with a track record who can work with the big players, who knows what is required to get in the Champions League and play a big role in it for years to come.
"Rafa Benitez is in Italy at Napoli but his family still lives in the North West and he has always made it clear that he would love to return to the Premier League at some stage."
Benitez famously clashed with then-United manager Sir Alex Ferguson during his time at Anfield but Hamann believes that he would do well at Old Trafford.
"The way it is going at Liverpool, I don't think he will be there any time soon and he has been at Chelsea so there are not too many clubs out there for him," the former Reds midfielder added.
"I don't think Arsenal will suit him. He and Manchester United would be a very good match. He had a few run-ins with Ferguson but he only pointed out a few facts, as he would say."