Pogba has fallen out of favour at Old Trafford since last month’s 6-1 defeat at home to Tottenham, starting just two of the seven fixtures that have followed.
Solskjaer appears set on deploying Scott McTominay, Fred and Bruno Fernandes in the middle of the park, meaning there is no room for Pogba along with new recruit Donny van de Beek and Nemanja Matic.
United triggered a one-year extension in his contract last month, with the previous deal set to expire next summer, but his lack of first-team action has once again plunged his future at the club into doubt.
And Deschamps believes the £89million star will be delighted to have linked up with France this week because of his current Red Devils woes.
“I know Paul well and he knows the squad well. He finds himself in a situation with his club that he can't be happy about, neither in terms of his playing time nor his position,” he told France Football.
“He's not at his best, he's had a string of injuries and Covid-19 has also affected him adversely. He needs to rediscover his rhythm.
“He did well in the matches that he was involved in last month and performed consistently despite his lack of rhythm. Nevertheless, we can't say that he's blossoming at club level.
“There's no problem with me, but I also work hard to manage him.
“When a player is unhappy at club level, of course he is happy to play for France. He will tell me about how he's feeling and as I know him very well, things will go in a positive direction.
“It's also his responsibility to put in a big effort.”
The latest murmurs of discontent come after Roy Keane felt the need to explain Pogba's shortcomings.
“Pogba’s performances over the last few years for United haven’t been good enough. It’s as simple as that," Keane told Sky Sports at the weekend.
"I know you make a point, Jamie (Redknapp), about players having energy and there’s an obsession at the moment with protecting the back four, but what United lack at the moment is a bit of creativity going forward.
"Bruno Fernandes has been brilliant, Donny Van de Beek hasn’t had a look in yet, I’d like to see him in there. Why not? I’ve seen Scott McTominay in there, Fred, Nemanja Matic - they’ve all had a go - but for me, they’ve not done enough."
Get the latest transfer news straight into your inbox!
Want to be on the ball with all of the latest football news?
Well then sign up for the brilliant new Daily Star Sport email newsletter!
From the latest transfer news to the agenda-setting stories, get it all in your email inbox.
How do you sign up?
It only takes a matter of seconds.
Simply type your email address into the box at the top of this article and hit 'subscribe'.
And that's it, job done. You'll receive an email with all of the top news stories every single morning.
You can find out more information on our email newsletter on this link here.
With Solskjaer telling talkSPORT after the 3-1 win over Everton: “You have to think you want to win the next one, you also look to the other one and, of course, Scott [McTominaty] and Fred didn’t play then because they were going to play this one.
“I thought Paul today, when he came on, he showed his character as well. He showed his quality and his strength that we could play the ball up to him, because we struggled in the second half.
“We were so tired, the rest of them who played in the week in Turkey, but Paul really freshened things up.”