World Cup winner Pogba returned after a month out with an ankle injury in a Carabao Cup tie against Rochdale last week and was involved in the 1-1 draw versus Arsenal on Monday, but United have left him out of their squad for their Europa League clash with AZ Alkmaar.
Manager Ole Gunnar Solskjaer described the issue as requiring "further treatment and rest" but Deschamps has suggested it is a "new" concern that could rule him out for close to another month.
"It's a new worry with his ankle," Les Bleus coach Deschamps said on Friday.
"He played in the [Carabao] Cup, he played again on Monday against Arsenal. He again has a problem that's going to keep him out of action for three weeks.
"I'd prefer he was there like all the available players but unfortunately he isn’t in a physical state to be present."
His return to action in United's shoot-out victory over Rochdale was followed by a 90-minute showing at home to the Gunners, the 26-year-old's 100th Premier League appearance.
Solskjaer's men travel to Newcastle United on Sunday, with their clash against Liverpool at Old Trafford their first scheduled fixture following the international break.
United lie 10th in the Premier League table after seven games and are three points off fourth-placed Arsenal, seven behind local rivals Manchester City and a further 12 points behind league leaders Liverpool.
Pogba seemed set to move on in the summer and has begun the season in indifferent form, recording just two assists from his six appearances across all competitions so far.