The England international, who is United's top goalscorer this season with 29 goals in all competitions, missed their last two wins against Wolverhampton Wanderers and Bournemouth, first with a leg injury and then an illness.
"It looks like (he will be available)," Ten Hag told reporters ahead of Thursday's home game against 12th-placed Chelsea.
"Yesterday he returned to training. He looks quite fit but we have to see today what is the outcome of the training, how did he recover, and then we will make our choices."
The Dutchman, who ended United's six-year trophy drought when they won the League Cup in February, said his team are on the right path but acknowledged that they are a work in progress.
After missing Champions League football last season, United are on track to secure a top-four spot in this campaign - they need a point from their final two matches against Chelsea and 10th-placed Fulham.
United are fourth in the standings with 69 points, three more than fifth-placed Liverpool, who have played a game more.
"We are in a project and we want to go back and win trophies," Ten Hag said.
"We win one trophy, but we want to win more trophies. We want to compete with the best, but we are still on a journey. But we think we are in the right direction. But we can always be better because good is not good enough.
"We want to compete with the best and then you have to be in the Champions League. So (it is) simple."
United have the chance to win one more trophy this season when they face rivals Manchester City in the FA Cup final on June 3rd.
