The England international is reported to have turned down a contract worth £100,000 a week and both parties have confirmed that talks on a new deal have been shelved until at least the end of the season.
With Sterling's future in doubt, the likes of Arsenal and Manchester City have been linked with a move for his services, but Liverpool boss Rodgers has no intention of letting his prized asset go.
"Raheem is not going anywhere this summer," he said. "As a club we've shown that [money does not come in to it]. If the club doesn't want to sell, it won't sell.
"I'm quite relaxed on it. It's part of the modern game. Raheem still has a lot of improvements. This a great place for him."
Sterling conducted an interview with BBC Sport that aired on Wednesday in which he stated he did not want to be known as a "money grabber" and suggested that he was stalling on a new contract because he was unsure if Liverpool can match his ambition to win trophies.
Rodgers stated that the club were unaware of Sterling's intentions to conduct an interview, but insists that the club can deliver his desire for silverware.
"For Raheem, it's purely about the football," he added. "What the kid is trying to do is put off talk about him being all about money.
"There was no permission from the club. It surprised us all. But he's a young player who is still learning.
"Raheem's ambition is to win trophies and that's perfectly aligned with what we're trying to do. This is one of the great clubs.
"The focus now is purely on his football. That's my only concentration. I said the intention of the player and the club was to put it [contract talks] on hold."
