Colwill, who has enjoyed a breakthrough campaign after joining from Premier League side Chelsea on a season-long loan last summer, has been sidelined with a knee problem since early January.
He was due to return to full training late last month, but was still experiencing pain and had an injection, which ruled him out for a further short spell.
But he could now return to the fray for the trip to face the Cottagers after missing the last games in all competitions.
Head coach Carlos Corberan, whose side are unbeaten in 14 matches in league and cup, said: "Colwill has made some days in training this week. Depending on today's training, we will make a decision with him."
Fellow Chelsea loanee Tino Anjorin is continuing to work with medical staff at his parent club with the midfielder in the final stages of his rehabilitation from a metatarsal injury.
Providing an update on the winter window signing, brought in to add another midfield option for Town in what could be a key run-in in their quest to finish in the Championship's top six, Corberan added: "Tino is not working with us yet and will continue with Chelsea where he will be working with the medical staff.
"The next step is working with us. We hope in the next week that he will start to work with our medical staff."
Corberan has revealed that Pipa will miss the trip to Fulham with a groin issue.
It is the latest blow for the Spanish full-back, who underwent surgery to correct a problematic hip injury last summer, with his first outing of the season coming in Town’s final game of 2021 at Nottingham Forest.
Pipa then lasted just half an hour of the FA Cup game with Barnsley earlier this month due to a groin issue, but was able to return for last weekend's derby with Sheffield United after missing the midweek game at Preston.
But Corberan has confirmed that the groin problem is still afflicting him.
Corberan continued: "Sometimes, when a player has had a long-term injury, they come back with different types of injuries and not the same one.
They start to have the consequence of not being on the pitch training normally. Pipa is not going to be available tomorrow because he has a small tear in the groin and we need to manage the minutes he has on the pitch very well and his training with the tam and the minutes he can play.
"We don't know if he will be available against Cardiff or Birmingham. Everything will depend on how he reacts to the medical treatment.
"We have the same squad available (for Fulham) apart from Pipa, with the possibiity of Colwill being available.