That is according to Don Balon, who claim the Manchester City boss favours a move for Bale over Arsenal forward Alexis Sanchez.
The Real Madrid star faces an uncertain future at the Bernabeu after a frustrating campaign last term.
Manchester United are interested in bringing Bale back to the Premier League.
And Bale could be moved on in a bid to raise funds for Monaco sensation Kylian Mbappe.
Despite his wealth of attacking options, Guardiola fancies adding the Welsh wizard to his squad after struggling to land Sanchez.
Arsene Wenger is refusing to sell Sanchez, who has less than a year left on his contract.
Both Manchester clubs are ready to launch £90m (€100m) offers for Bale.
And Don Balon claim Real are in a rush to sell so they can finalise their own deal for Mbappe, 18.
Bale managed just 27 appearances in all competitions last term due to a number of injury problems.
The 28-year-old even lost his place in the team following the emergence of Marco Asensio.
Wales legend Ian Rush has urged Bale to stick it out at the Bernabeu.
“If he’s happy then Gareth should stay in Spain, 100 per cent," Rush said. "He has improved as a player.
"He’s got great players like Cristiano Ronaldo to keep learning from. There are not many better clubs in the world than Real Madrid.
“I know that if he decided to come to England he would have the choice of all the top clubs here.
"Manchester United, Manchester City, Chelsea, Arsenal and Liverpool would all want him.
“There’s always a time and a place to come back but I don’t think it should be now. He is still relatively young.”
Meanwhile, the Sunday Express are reporting that Chelsea are also interested in Bale.
