The Spanish striker has been out with a groin strain, that he sustained during the home defeat to Blackpool earlier this month.
Liverpool's head of sports science and sports medicine Peter Brukner told Liverpoolfc.tv: "Fernando is doing pretty well. He had a slight tear in one of his adductor muscles very early on in the game against Blackpool that prevented him going away with Spain in the internationals.
"He has had intense treatment over the last 10 days and responded very well to that treatment. He's ready to resume training today and if we can build up his training and get through the next few days, then we are optimistic but not certain that he will be able to line up against Everton.
"It's still early days but so far so good. He has responded well to the treatment but we will just have to wait and see whether he is able to build up his training sufficiently.
"He'll join in the full training session on Thursday, then build up Friday and Saturday. If he gets through these sessions and he is able to stretch out fully and has no after effect from the sessions then he will be able to play.
"So we are optimistic he will be ready but it's still too early to say for sure."
Liverpool will wait until Saturday to decide whether Torres will feature against Everton at Goodison Park.
He added: "The medical and fitness teams will make a joint decision based on the assessment of the player. I'll take that to the manager and discuss with him, and he always listens to what we say."