Pogba continues to be linked with a move away from United, with Barcelona said to have had a bid rejected for the France international, who is now a World Cup winner.
Dembele, meanwhile, will see his Tottenham contract expire next summer, and it is understood that the Belgium international is keen on an exit.
A number of Chinese Super League and Italian clubs have been linked with Dembele, but Merson has insisted that United should be in for the 31-year-old.
"I'd buy Dembele tomorrow morning. He's one of the best players in the Premier League," Merson told Sky Sports News. "If I was Man United, I'd sell Pogba tomorrow morning for £100m and buy Dembele. All day long. I think Dembele's up there with the best of the best."
The Premier League transfer window for this summer will close at 5pm on Thursday.