Manager Ole Gunnar Solskjaer has a re-building job this summer with the likes of Grealish, Jadon Sancho and Donny van de Beek linked with a move to Old Trafford - and United legend Giggs said that Grealish would be a good fit at the club.
"I mean, if a quality player like that comes available, United are going to be [interested]," Giggs told Premier League Productions of Grealish.
"He looks like a United player, he takes the ball, he attracts loads of fouls."
He added: "I would say that we definitely need a centre-forward.
"Someone who, if a team is deep, is going to play deep and be on the end of those passes, crosses and score 25 goals.
"I still think if we're going to catch City, we're three or four players short.
"But [it's] definitely exciting and promising with Bruno [Fernandes] and [Paul] Pogba coming into the team."