Bale has been a long-term target for United and cast doubt over his future after a starring cameo in last month's Champions League final when he suggested that he needs to be playing more regular first-team football.
Zinedine Zidane's shock departure as Madrid boss could have an impact on whether the Welsh winger stays in the Spanish capital, but United are still understood to view Bale as their main transfer target.
Spanish publication Don Balon claims that manager Jose Mourinho is even willing to offer Pogba - who returned to the club in a then-world record £89m deal in 2016 - plus cash in exchange for Bale.
Madrid are thought to value Bale at more than £100m, with some reports suggesting that it could cost United as much as £320m to prise him away from the Bernabeu.
Pogba's future at Old Trafford has also been the subject of much debate following reports of a falling-out between the France international and Mourinho.