Pogba joined United in an £89m deal from Juventus in the summer of 2016, and the France international has impressed in spells for the Red Devils.
The midfielder's form has been called into question on a number of occasions in recent weeks, however, and it has been suggested that United boss Jose Mourinho could look to sell the 24-year-old at the end of the season.
Verratti, meanwhile, is said to be considering his future at PSG following their failure to make an impression in the Champions League once again.
According to The Independent, Mourinho would be open to allowing Pogba to leave if it meant landing Verratti, but any deal is believed to be some way off despite the two players sharing Mino Raiola as an agent.
United will look to bounce back from their shock Champions League exit to Sevilla when they host Brighton & Hove Albion in the quarter-finals of the FA Cup this weekend.