Milner, who won the Premier League title with City before joining Liverpool, wants United to do bitter rivals Liverpool a favour by beating City and increasing the pressure on them in the final weeks of the season.
"First time in my life," Milner told reporters when asked if he would support United over City. "But I won't be watching. It's a bit of a waste of energy, willing the ball in the other goal."
City will be crowned champions if they win their remaining games, while Liverpool need City to drop points if they are to end their 29-year wait for an English top-flight title.
"They're a top team, they've done it before and are grinding it out. All we can do is win the rest of our games and put them under pressure," Milner added.
"There's three games left after (United). People think United is a challenge, but it's not the only one. It's an old cliche but the Premier League is tough whoever you play."
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Simon Jennings)
