The Red Devils are understood to be interested in both English attacking midfielders this summer, although they are likely to only move for one, with Grealish reportedly at the top of their list.
The Aston Villa skipper has scored seven goals and registered six assists for the relegation-threatened Midlands outfit this season compared to six goals and three assists from Maddison, and Greening believes that the Leicester playmaker is too similar to January signing Bruno Fernandes.
"Over the past few months there's been talk of Grealish coming or Maddison coming. I actually feel I would prefer Jack Grealish," Greening told Metro.
"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 two, three players in one movement. He'd be a better player at United with the current squad than Maddison would be for me."
United are understood to be reconsidering their £80m interest in Grealish after the Villa man was allegedly involved in a car crash while flouting government guidelines to stay at home during the coronavirus lockdown.