City have agreed a price of £49million for the England man, who now will discuss personal terms and take a medical.
Rodgers said: “The situation is very simple. The club has agreed a deal with another club for Raheem subject to a medical that’ll 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’s no issue there.”
Sterling, who has been chased by City all summer, turned down a new Anfield contract earlier this year and twice failed to report for pre-season training last week, blaming illness.
City had reportedly already failed with two bids for the forward, with the second believed to be around £40million, but now Manuel Pellegrini’s men have agreed a deal and are set to offer the 20-year-old around £200,000 a week.
Rodgers has already been busy in the transfer market, and new boys James Milner, Danny Ings, Nathaniel Clyne, Joe Gomez and Adam Bogdan are all 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.
Rodgers said: “He’s a top class player. He’s played in Europe, so he understands it.
“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.”
Liverpool missed out on Champions League football with a sixth-place finish last season but Rodgers refused to be drawn on what his target is for the season.
He said: “At this moment in time, our objective is to get as fit as we possibly can. And then next season, the target is to be the best that we can possibly be.”