Pogba, currently a free agent, will be eligible to play again from March after his four-year doping ban was reduced to 18 months.
As he nears a return to action, several clubs, including Marseille and Fiorentina, have reportedly turned down the chance to sign him.
Despite this, former United defender Rio Ferdinand has called on manager Ruben Amorim to offer Pogba a trial, while Saha fully supports the idea of a reunion.
He believes Pogba remains one of the “best players in the world” and could still make a significant impact at Old Trafford.
If Manchester United were to re-sign Pogba, it would mark his third spell at the club.
The 30-year-old first left United for Juventus in 2012 before returning in 2016 for a then-world record fee. His second stint was marred by inconsistency and injuries, but Saha and Ferdinand believe he deserves another chance.
“I would take Paul Pogba back at Manchester United in a heartbeat. It’s not only because of the squad that we have now with injuries and all that but for all the elements that he brings as a player,” Saha told Best Betting Sites.
“We need guarantees, we need quality, we need confidence, we need leadership, and this guy now has an opportunity to show how much he wants it.
“Pogba can show he can be one of the best in the league in this position, especially with the motivation and the focus that he has to understand where he can improve and what parts of his game he needs to adapt.
“It’s an opportunity to sign someone highly motivated. He’s going to obviously still have huge confidence in his ability. I’m sure that when he looks at this midfield at United, he has a different type of vibe in his game.
“So definitely it’s an easy fit… I’m sure Pogba wants the visibility. He wants to go back to a French team as soon as possible, so he just needs to pick the right project.
“For him to get back into the national team, he needs to show that he can still do it at the top level. United would be signing a player who is completely dedicated and focused on achieving his goals because he’s been out of the game for so long.
“I’m sure that the most important thing for Pogba would be to show Amorim and the Manchester United fans that he is still one of the best players in the world.”