Leeds lost their top-flight status back in 2004 and are yet to return, with the club seemingly struggling to pick themselves up from that setback.
It has led to Milner, who broke through at Elland Road before moving to Villa, stating that he believes the Whites' plight can act as a warning to the Claret and Blues.
Villa are still not clear of safety, although they have improved under Tim Sherwood, and Milner insists that reputation is no guarantee of survival.
“It’s true that it doesn't matter how big a club is because anyone can go down – look at Leeds United – but it’s pleasing to see them recover from where they were because they're a good club, I had a lot of good times there and I still know a lot of people at Villa," Milner said.
Milner is preparing to face Villa this weekend, with his City side due to welcome Sherwood's men to the Etihad Stadium.
Earlier in the season it would have looked like a routine home victory, but Villa should cause City a number of problems if they can maintain the level of performance they have displayed of late.
The Midlands outfit have showcased the potential that they have in their squad over recent weeks and they will be looking to pull off another upset when they take on City.
If they can, then Sherwood's side will feel relatively assured of their Premier League status, as they are likely to extend their current advantage over the bottom three with a win.