The manager felt fatigue played a part in Saturday's home defeat to Aston Villa, and Sterling has featured 25 times already in his first season as a regular.
Now Rodgers wants to avoid overplaying the 18-year-old, whose form has earned him international honours with England.
"There is no doubt Raheem is one who does need that breather," he told the club website.
"I've thought about it over the past couple of weeks. In order to do that you need to have that depth to take him out and put somebody else in.
"That's something I'm thinking about - who to put in. He's a naturally very, very fit boy but he needs that mental rest as well. That time will come and he will get the breather soon enough.
"Joe Allen is another one. If we're honest, there are a few who could do with that breather, especially mentally. It's something for sure I need to have a wee look at."
One player set to play throughout the Christmas period is Luis Suarez. Rodgers said: "He's at his best when he is playing regularly."
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