Sterling had asked to leave Anfield and was the subject of two bids from City in June, which were rejected. The player was reported to have said that the breakdown of his relationship with his manager was one of the reasons for wanting to leave.
Rodgers said: “The situation currently is simple. The club has agreed with another club a deal for Raheem to be transferred. Subject to a medical, that will go through.
“Contrary to the last week or so, in terms of what was written, Raheem and I have always remained very strong in our relationship, and have been up until he left. There is no issue there.”
That is not what the Sterling camp has been whispering as the England international is not bought into the direction that Rodgers is taking Liverpool.
Rodgers has already been busy in the transfer market and new boys James Milner, Danny Ings, Nathaniel Clyne, Joe Gomez and Adam Bogdan are with the squad on the tour.
Roberto Firmino is still on holiday following the Copa America but Rodgers is delighted to have secured the services of the Brazil international from Hoffenheim.
“He’s a top class player. He’s played in Europe, so he understands it” said Rodgers.
“There’s no pressure. He’ll come in to the PL, and it will take time to adapt. But he has all the traits and the profile that we would want. He works hard, has talent and can score goals. We’re really excited.
“It was important to improve and build the squad for the season. We’re very pleased with the players we’ve brought in.
“The key for us is the overall team. Individuals like Raheem will have benefited from the team. We aim to be much stronger and more competitive than we were last season, and we’re relying on everyone.
“The focus has been really good, the start has been strong. Hopefully we can remain that way over pre-season and take that confidence into the new season.”