The Welshman is expected to leave the Spanish club this summer after Zinedine Zidane made it clear he’s no longer wanted.
The Frenchman revealed this week that Bale refused to come on during Real’s clash with Bayern Munich on Sunday.
And reports have suggested a number of Chinese clubs are lining up mega-money offers.
Bale is currently Real’s highest earner on almost £300,000-a-week and Los Blancos may find it difficult to add to their squad while he’s still there.
Zidane is still in the market for a midfielder and sees Pogba as the ideal target.
And according to Spanish outlet Mundo Deportivo, Real will look to bring the United star in once Bale leaves.
The report claims the Red Devils will not sell for less than €200m (£179m).
Mundo Deportivo also state that Real will have to move quickly if they plan to sign Pogba.
“Gareth is one of the best players on the planet.”
Jonathan Barnett, Bale’s agent
The transfer window in England closes in just over two weeks.
And United will not sell if they don’t have time to draft in a replacement.
There have been suggestions that Bale could leave on loan to free up some of his wages.
Bayern Munich and PSG have both been linked as potential destinations.
But the 30-year-old’s agent, Jonathan Barnett, has made it clear that won’t be happening.
“There will be no makeshift deals to get him out of the club,” he said.
“Gareth is one of the best players on the planet.
“I can guarantee you he will not be going on loan to any club.”