Standard Sport understands both players are of interest to Ole Gunnar Solskjaer, though Jadon Sancho is the main target over the Aston Villa and Leicester City midfielders.
Former United man Jonathan Greening believes Grealish would be a better fit than Maddison following Bruno Fernandes's arrival.
"Over the past few months there's been talk of Grealish coming or Maddison coming," Greening told Metro.co.uk.
"I actually feel I would prefer Jack Grealish. Maddison is a very good player, super technical, he can create, great passing both short and long, and great on set plays.
"Jack Grealish, however, has that little bit of difference, he can take players on, he can drive forwards with the ball, and slide that pass through. He's got that bit of grit and determination; and doesn’t like losing, you can see that in his game.
"Maddison is also maybe a bit too similar to Fernandes, whereas Jack Grealish will bring in something different, he can find pockets of space, he can drive at opponents and take on 2-3 players in one movement.
"He’d be a better player at United with the current squad than Maddison would be for me."