Pogba’s contract at Manchester United expires at the end of this season.
The French midfielder has failed to make a big impact once again this season and he has been subject to criticism for not replicating the form he shows with the national team.
The 28-year-old will have his contract run out next summer and United are reportedly keen on extending his stay.
Whelan said: “Paul Pogba has put himself in this position with his performances for Man United. He’s been awful for a long time now.
“There have been flashes where he’s seemed to be that quality player they spent all the money on. Bar that, he’s been quite average.
“Look, he’s not done enough to stay at Man United. If they can get some money in January, perfect.
“The changing room will be better off without him in there. They need different characters at the club now to stride forward and be successful. And Rangnick knows that.
“Rangnick has to break the stigma at the club about big-money signings underperforming.”
Pogba is currently recovering from a thigh injury he picked up during the international break months ago.
Man Utd are said to have proposed a new deal but the Frenchman is yet to make a decision on his future.
Real Madrid and PSG are monitoring his situation ahead of a potential free transfer next summer. Furthermore, he will be allowed to hold talks with clubs outside England next month.