Pogba has been restricted to just eight appearances in all competitions during an injury-plagued 2019-2020, while rumours persist of an end-of-season exit from Old Trafford.
Real Madrid and former club Juventus have been tipped to make a move for the France international, yet ex-United goalkeeper Bosnich can see the player staying put.
"If I had to put money on it right now, I think he will stay, I really do," he said. "If you've got a player in the dressing room, regardless of whether it's Paul Pogba or Paul Smith, you let them go in the most amicable way possible.
"There's no use carrying someone who doesn't want to be in your club because it affects their performance and it can start to affect the performances of people around them."
Pogba is closing in on a comeback but it may be further delayed by the coronavirus-enforced shutdown of Europe's top competitions, with no return date in sight for the Premier League.
United had gone 11 matches without defeat before the season was halted, its upturn in form credited to the arrival of January signing Fernandes.
Bosnich suggested Pogba will be walking into a different side to the one he last played in.
"There's no doubting [Pogba is] a world-class player," he said. "I watched him live at the World Cup in 2018 and I thought he was phenomenal.
"With the arrival of Fernandes and the team winning and playing well, it makes a huge difference.
"If he (Pogba) can come back and play to his full potential, that is fantastic news - not only for him and Fernandes but for Manchester United and all their supporters."
Fernandes has hit the ground running with three goals and four assists for United in his first nine appearances, earning praise from Bosnich.
"He's a superb signing. Anyone who had followed him at Sporting would have seen what a top player he was," he said. "Even if you didn't watch that many games in Portugal, you looked at the stats - his goals and assists.
"I don't think anyone in their wildest dreams imagined he would settle so quickly. But it's great for him, great for the club and great for Ole Gunnar Solskjaer.
"I'm really happy for the player and for the club and really looking forward to them coming back."