Griezmann was heavily linked with a move away from Atletico Madrid in the summer.
Manchester United were reportedly considering triggering his £88million release clause, but he opted to stay due to Atletico’s transfer ban, which meant they couldn’t sign a replacement.
And now Spanish outlet Don Balon claim Atletico’s cross-town rivals Real Madrid are desperate to sign Griezmann.
Real are said to be willing to sell Bale in order to raise funds for the France international.
Atletico will reportedly be forced into selling Griezmann with the imminent arrival of striker Diego Costa from Chelsea.
Don Balon add that United could be Bale’s next club, with Mourinho openly discussing a move for the Welshman during the summer.
The Old Trafford manager revealed before United’s Super Cup defeat to Real Madrid that he would fight for Bale’s signature if the 28-year-old was left out of Zidane’s line-up.
Asked about trying to buy Bale last month, Mourinho said: “Well if he’s playing tomorrow, no.
“It’s because he’s in the coach’s plans and because he also has that motivation to continue at Real.
“If he is not in the club’s plans, that with the arrival of another player would mean he was on his way out, I will try to be waiting for him on the other side and fight with other coaches that would want him.
“But if he plays tomorrow, that is the best confirmation he is wanted by the team.”