Hummels has been identified as a key target by the Red Devils and it is expected that the club will make an official approach to acquire his signature in the summer transfer window.
But Hargreaves, who spent four years at Old Trafford and made just 39 apparances due to a number of injuries, says that while the Germany international is "the new Franz Beckenbauer", he is not the right man to reinforce the United defence.
"He's a super, super ball-playing centre-back but I don't think he can defend, he's too slow," he told BT Sport.
"He's Franz Beckenbauer, the new version, a super passer but I think that if I'm Manchester United I want [Nemanja] Vidic, I want [Vincent] Kompany.
"I think he's a nice football player, he's easy on the eye, but United need somebody physical, a presence.
"He's the captain of Borussia Dortmund, they're last in the Bundesliga. Is that the measuring stick for Manchester United? I'm not so sure."
