The Reds are reluctant to risk the long-term fitness of their teenage forward and would be happy to offer him an extended period of rest.
Sterling has been taken out of the firing line on a regular basis since bursting onto the Anfield scene at the start of the season.
Rodgers is reluctant to see the 18-year-old burn out so early in his career, especially as he is struggling with a knock.
It is possible that Sterling will not figure again in Premier League action this term, and that would cast doubt over his involvement at this summer's European Under-21 Championship with England.
Rodgers said: "Raheem has an ongoing problem with a small tear at the top of his thigh.
"It has worsened and is something that, if he plays, could end up bigger and creating problems as he gets older.
"So we've a duty to the boy not to store up a problem for later.
"We felt it would be best to give him a two-week breather from the training to protect the injury. If he needs to rest until the end of the season, then that'll happen."