The Republic of Ireland international suffered an injury to a cruciate ligament playing for his country against Kazakhstan in September having made just one appearance for his club this season.
Manager Roberto Martinez has remained optimistic the 26-year-old could return before the end of the campaign and he will start taking tentative steps towards that in the near future.
"Darron is working well and is going to join the group very soon," said the Toffees boss.
"Then it's about seeing how he can adapt to the demands of working with the group.
"He is out on the grass, though he hasn't joined in with the group yet. That's not going to be too far away with how he is recovering.
"The one-to-one work is showing really well and I don't think he is going to be too far away from joining in with the group, which is a real success in itself."
Martinez said Gibson had progressed quicker than expected and playing again this season would speak volumes about the midfielder's character.
"He is well ahead of schedule and that always pleases me, to see a player get ahead of the timing because it shows all the hard work they put in behind the scenes when nobody is watching," the Spaniard told evertontv.
"The desire of Darron has been sensational in that respect and to have him around the place is a great sign.
"It will be great for him to be involved one way or another before the season ends, even though that would be an incredible and remarkable achievement since looking back on when the injury happened with the national team."