Wales international Bale has won 10 trophies since joining the La Liga giants from Tottenham four-and-a-half years ago.
But Florentino Perez has faced calls to cash in on him due to a series of injury problems.
The Real president refused to move Bale on in the summer because he had faith the winger would leave those issues behind.
Bale has continued to struggle this term though and the latest reports suggest a price tag has now been slapped on him.
According to Diario Gol, Real will only sanction a move if a club stumps up £79m.
The Spanish outlet say there are two sides interested in getting Bale on-board.
United would apparently enter the bidding, with Jose Mourinho having talked up the 28-year-old in August.
Tottenham, likewise, are keen on Bale as they look to strengthen their squad.
Spurs chiefs are only willing to pay £53m (€60m) for the Southampton academy graduate.
However, that stance could change if Bale manages to prove his fitness.
Bale will be hoping to guide Real to the Club World Cup title this evening.
Zinedine Zidane’s men face Brazilian outfit Gremio in the final at 5pm.