Sterling was left out of the squad for Liverpool‘s pre-season tour to Thailand over the weekend after the two clubs finally settled on a fee – believed to be £49million – for the England forward.
The 20-year-old is understood to be undergoing a medical at City on Monday although Press Association Sport understands no official confirmation of the deal is imminent.
Speaking at a press conference in Bangkok, Rodgers said: “I spoke to Raheem at length again before I left yesterday, so there is no issue and no problem.
“Two clubs have agreed a deal and subject to a medical he will move on. But at this moment in time the interest is with the players that are here.”
Liverpool rejected two initial City bids but once it became obvious they would increase their offer a third time, Sterling was dropped from the tour party on Sunday.
And the expected confirmation of Sterling’s arrival at the Etihad Stadium later this week will bring an end to a six-month saga which has been acrimonious in spite of Rodgers’ insistence that his personal relationship with the player remains intact.
Sterling angered club officials in February by rejecting what Rodgers described as “an incredible deal” – then engaged in an unsanctioned interview with the BBC two months later in which he confirmed he had turned the offer down.
The impasse deepened when Sterling’s agent, Aidy Ward, claimed the player would not sign even for “£900,000 a week”.
Sterling missed the start of pre-season training last week, citing illness as he sat out Wednesday and Thursday’s sessions before returning on Friday.
He was initially included in the club’s tour party – despite reports that he had asked Rodgers to be excused – before City’s move made his departure inevitable.