Rodriguez has scored three goals and provided three assists in the 10 matches he has started this season and Ancelotti said he could tweak his formation in the absence of the Colombian when his ninth-placed team welcome Chelsea to Goodison Park.
"James had a little problem during the game against Burnley. He had a problem with his calf and wasn't able to train this week. It's nothing special," Ancelotti told reporters.
"I think he'll start to train next week but for this game I don't want to take a risk. We have to look at him... to see if he'll be available to train and play against Leicester (on Wednesday).
"James is a fantastic player for us. But we'll be able to adapt to the fact he's not going to play. We have a good squad and maybe we're going to play a little bit differently."
Ancelotti said captain Seamus Coleman was back in training after overcoming a niggling hamstring issue but the clash against third-placed Chelsea comes too soon for the defender.
Everton will also be without midfielder Fabien Delph who sustained a similar problem to the full back.
Ancelotti said he was looking forward to the clash with his former club Chelsea now managed by Frank Lampard who played under the Italian at Stamford Bridge.
"He's doing really well, before Chelsea, and did well this season and last season... now, he has a fantastic squad and fantastic team," Ancelotti added.
"Our relationship has changed, it was between manager and player and now a relationship between colleagues. I'm pleased to see him again."
