The France international has been heavily liked with a move away from Old Trafford in recent months.
And according to Spanish news outlet Don Balon, Pogba could be heading to Real in a swap deal for Bale.
They say Jose Mourinho is willing to include his £89m midfielder in a player-plus-cash deal to land Bale this summer.
Don Balon reckon Mourinho’s relationship with Pogba is beyond repair and he’s willing to sell the former Juventus star.
Bale put Mourinho on red alert after Real’s Champions League final win against Liverpool, with the winger revealing he may leave the Bernabeu to get regular game time.
Pogba, 25, has been vocal on Mourinho and his United future in recent weeks, with the France ace refusing to rule out an Old Trafford exit.
“He [Mourinho] put me on the bench, I answered on the pitch, I give my maximum every time,” he said.
“There are times when I wasn’t playing. I was on the bench. Much has been spoken about.
“People thought it was wrong but a coach and player don’t have to be best friends.
“One is not forced to go to the restaurant together. I had some problems, it’s [a] mental [problem].
“It made me grow in leadership. I had the armband with Mourinho, it was the first time in a club.
“It’s important to me, it makes me grow up to be as a leader in the France team.
“Stay at United? You’re never sure of anything. Contractually, it’s on, yes.
“Walking on the Parc des Princes? With a club, no for sure. Honestly, it doesn’t appeal to me.
“I grew up here, my father was a supporting Marseille and so did my mum. Paris wasn’t really in my daily life.”