The Old Trafford legend believes his old side should be chasing the Real Madrid star, who is also reportedly on Arsenal's radar.
Ex Manchester United striker Andy Cole, the Premier League's second highest goalscorer, has picked the player he thinks his old club should target to improve their attack, telling the Mail that Real Madrid forward Karim Benzema would be an ideal strike partner for Red Devils captain Wayne Rooney.
And though there is some debate whether he would have split loyalties, the Frenchman is a player Cole's boyhood club Arsenal are also said to be chasing, according to the Star.
"I like him (Benzema)," Cole told the Mail. "He's a very good player and played at the highest level for numerous amount of years.
Cole scored 121 goals in eight years at Old Trafford, and feels the Manchester giants should be targeting someone with consistent, proven quality of performing at the very highest level, as Benzema has done for Real, rather than going with some who is early in their career, like Harry Kane.
"He's done it at international level and (you) look at that and say that could definitely work and him and Rooney," Cole added on the former Lyon striker.
"I think the kid (Kane) is talented, but we have to be honest. He's had half a season where everything went for him. Penalties at the keeper and rebounds are coming straight to his feet.
"He's scored some goals but to take that leap - because your second season in the Premier League is always tough - to leave Tottenham and come to Man United and for Man United to pin all their hopes on him, for the money and if it did happen, that's a hell of a lot of pressure."
Kane scored 31 goals last season for Tottenham, with the 21-year-old finding the net more times than any other player has done in 23 years for the North London side.
By comparison, Benzema scored 22 times in 46 games, though he has managed to score 20 goals or more in each of the last five season in Spain.
With 214 goal in total in his career, Cole clearly feels Benzema is the right kind of established quality for United to be considering, but with the player's agent stating to the Mirror recently that he wouldn't leave Madrid unless he was told to, maybe he is worth involving in any possible deal for David de Gea, if the goalkeeper digs his heels in regarding a return to Spain.