Pogba produced another brilliant performance for France on Wednesday night when the world champions beat Croatia in a UEFA Nations League clash.
The Frenchman has been a pivotal part of the national team and played a big part in France winning the World Cup two years ago.
But he has remained frustratingly inconsistent for Manchester United and has attracted criticism for his performances in the middle of the park since the start of the season.
Leboeuf believes France coach Deschamps knows how to get the best out of Pogba and the midfielder feels more comfortable in the national team as everyone trusts him to do well.
The former World Cup winner insisted that Solskjaer must learn from his France counterpart on how to motivate the midfielder to give his best and retool his coaching style if necessary.
Leboeuf said on ESPN FC: “There is maybe a way to understand Paul Pogba and to make sure that he gives his best for you.
“And maybe Ole Gunnar Solskjaer and [Jose] Mourinho before him didn’t get it. For sure, Mourinho didn’t get it and they argued a lot.
“I think Didier Deschamps exactly knows how to handle Paul Pogba and how to make sure he gives his 100 per cent.
“And that may be the best task Ole will have to do if he wants Paul Pogba at his best.
“It works for the national team only because he feels good, he feels important, he feels free and he feels that people trust him.
“And that maybe not the case at Manchester United.
“I don’t say that it is only the others’ fault and maybe a lot of it is Pogba’s problem, but that’s how it is and you have to cope with the situation.
“A good coach will work with the player that he has and not with the philosophy of football.
“You have to work with the squad that you have and make sure you get the best out of them.”
Solskjaer will be looking for Pogba to up his performances for Manchester United as he bids to drive the Red Devils into form.