The club have tabled what a couple of weeks ago Rodgers described as an “incredible” offer – reported to be in the region of ??100,000 a week.
A few weeks before that the Reds boss had suggested an agreement was imminent but latest reports suggest there has been no movement in negotiations.
Sterling only signed an improved contract in December 2012 and his current deal does not expire until 2017, which is why Rodgers is content to play a waiting game.
“There is nothing new to report on it. I am quite relaxed about Raheem’s situation,” said Rodgers.
“He is not going anywhere in a hurry – he has still got this season and another couple of years to go on his contract.
“I think it is quite obvious when you look at Raheem’s situation anyone with Raheem’s best interests would see Liverpool as the best option for his career.
“He turned 20 in December and he has made 114 appearances, which is a remarkable amount at a club of this size to be given that opportunity.
“He has made it clear himself that he loves being here and I think he was quoted as saying this is the best place for any young player to develop, so that makes me quite relaxed.
“I am sure the club and his representatives will find the solution for that.”