According to Rob Dawson of ESPN.co.uk, Pogba pulled up in training on Friday and now faces a late fitness test on Saturday ahead of the lunchtime kick-off.
Dawson added that, while the French midfielder was unable to finish the session at Carrington, he has yet to be ruled out, and there remains hope he could face Jurgen Klopp's Reds.
Pogba, 24, is not enjoying the best of spells with United. He started on the bench for recent matches against Huddersfield Town and Sevilla and has been some way from his best even when he has started.
He has not scored a goal or provided an assist since January 15.
However, the £89 million man remains a crucial part of Jose Mourinho's side, and it will be a big blow for the Red Devils if Pogba is unavailable to face Liverpool.
United can call upon Ander Herrera and Scott McTominay to provide cover, but neither player can produce the kind of game-changing performance Pogba is capable of when at his best.