Milner is reportedly set to depart the Etihad Stadium with the Reds in pole position for the 29-year-old but at his pre-match press conference ahead of this weekend's Premier League clash against Sunderland, he said he would not comment on players until they had signed for his club.
The Liverpool boss said: "James is a wonderful player. But players get linked with the club consistently."
He was asked about the contract situation over Raheem Sterling but said it was between the players representatives and the club, and said added comment on more questions surrounding Steven Gerrard.
Rodgers told reporters: "No doubt Steven is still a world class talent. Club has to keep moving forward. Opportunity for others to grab the mantra."
The Liverpool boss added there needs to be a plan in place players the club of the highest, like Gerrard.
One big positive for Liverpool is that Daniel Sturridge is about to return to the UK after undergoing rehabilitation in the United States on a thigh injury which has plagued his season so far.
Rodgers gave an update on when he should be available, saying: "Daniel is a top class player. He has wonderful qualities. Will make any team better. We're hoping he can stay fit and make charge for us
"We're hoping that in some point in January he'll be back in the squad.
Rodgers said there are no additional injury worries ahead of this weekend's trip to the Stadium of Light as his side go in search of a win to improve their chances of qualifying for the Champions League next season, and of only their fifth clean sheet this season.
He said: "We have a tendency at times to make mistakes and concede silly goals."