The ex-Germany international, who played under Benitez at Anfield, believes that the Spaniard's track record of winning trophies makes him an ideal successor to the ousted David Moyes.
"It is certainly a name they should consider. 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," Hamann told talkSPORT.
"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."
He added: "If I was a United fan I would want somebody who gives you the best possible chance to get back in the Champions League."
Louis van Gaal, Carlo Ancelotti, Diego Simeone, Jurgen Klopp and Pep Guardiola have all been linked with the Old Trafford hotseat, while interim manager Ryan Giggs is thought to be in with a chance of landing the role on a permanent basis.