Pep Guardiola’s defending champions have spent much of the 2018-19 campaign playing catch-up.
Rivals at Anfield have occupied the top spot for long periods, with Liverpool’s solitary defeat through 25 games coming at the Etihad Stadium.
City were, however, to move back to the summit on Wednesday as they prevailed 2-0 over Everton on Merseyside to edge back in front of the Reds on goal difference.
It is now up to Jurgen Klopp’s side to offer a response to being knocked off their lofty perch, with recent outings having shown signs of nerves from a club that has gone almost 30 years without tasting title glory.
Former City defender Mills told Sky Sports of the latest twists and turns in a thrilling battle for domestic supremacy: "Liverpool have had a bit of a blip, I think that's all it is at the moment. But the pressure has swung massively in Man City's favour.
"Liverpool had a nine-point lead not so long ago, that's gone. For City to go ahead, even when they've lost recently, the likes of the Newcastle game, now the pressure is all on Liverpool.
"City have been there, they've done it, they've won the league several times in the last few years, Liverpool are approaching 30 years since they last won the title - it's the last little hurdle to finally get it. Can they do it?
"It's maybe a bit of belief, the manager's done it in Germany but not too many of these players have. There's one or two nerves creeping in now, but Pep's City just play.
"They are bothered about results, but he says play this way no matter what, and it brings results ultimately. Liverpool don't have that luxury."
Liverpool, who now boast a game in hand on City, will be back in action on Saturday when they play host to Bournemouth.
A positive result in that fixture will take them back to the top prior to Guardiola’s side taking in a testing home date with top-four hopefuls Chelsea on Sunday.