Bolton have completed the capture of former Crewe striker Max Clayton on a three-year contract.
Felix Magath has been sacked by Fulham, with Kit Symons taking over as caretaker manager.
Contract negotiations are ongoing between the Reds and Sterling, who on Saturday turned 18, the age at which players are permitted to sign long-term deals with clubs.
There have been reports the player and club are some distance from an agreement following Sterling's meteoric rise this season, but, despite the apparent interest of other top clubs, Rodgers believes it would be wrong to cave in to any high wage demands.
Rodgers said in the Daily Telegraph: "I don't want the club or the kid being affected by over-the-odds demands.
"I think there's a value I see in a young player that hasn't achieved anything. All the figures that get bandied about for kids these days can destroy them. I'm in the business of trying to help nurture these kids, and money distorts the reality. It's just one of these things that will get done. I'm confident that it will do.
"There's still 18 months left [on his current deal]. He's a young kid and we just want to make sure that everything's right for him to be nurtured. With young players contracts get handed out left, right and centre to a kid who's not done anything, getting a four-year deal on decent money, and then clubs wonder why in two or three years it's gone wrong.
"It's gone wrong because you've taken away his hunger."
Rodgers added: "There's good conversations so there's no worry or concern. It will be resolved."