Pogba faces an uncertain summer at Monaco, having managed only six appearances and 115 minutes on the pitch during an injury-hit first season back in club football.
Pogba joined the Ligue 1 club as a free agent last June after his four-year doping ban was reduced to 18 months, signing a two-year contract. But calf, thigh and ankle problems wrecked his first campaign back, restricting him to a single start and ending any hope of forcing his way into France's World Cup squad.
The 33-year-old is believed to earn below £44,000 a week at Monaco, a fraction of the £290,000 he was paid during his second spell at Manchester United, though the club could still look to move him on this summer as they work to reduce their wage bill under DNCG financial regulations.
Monaco chief executive Thiago Scuro did not rule out a departure when asked about Pogba's situation.
"It is a complicated topic because we have a lot of respect for Paul, for the person he is. Since he arrived, he has been very positive," Scuro told Get French Football News.
"It is also true that, last year, the project didn't work well because when we started with him in the summer, the expectations were very different to what happened.
"I think that we have to be fair with him, follow his preparation every week, how he will progress physically and technically, and then it will be the manager's decision.
"We have the summer to see what level we will see from Pogba. He could leave at the end of the summer. With Paul, it has always been a very open and transparent relationship. If, at some point, the expectations of the player are different to the expectations of the club, we will have to speak to find a solution. The performance will give all the answers that we need. Maybe he will stay, maybe he will leave."
The comments came as Monaco confirmed Filipe Luis as their new head coach, with the Brazilian set to have the final say on whether Pogba features once pre-season training gets under way.