Real Madrid want to sign Mbappe, with Arsenal and Paris Saint-Germain also eyeing the forward.
Express Sport understands it could be Bale who is sacrificed to fund a £120million move for the Frenchman.
But Bale has told Marca that he would be happy to see 18-year-old Mbappe join him at the Bernabeu.
“I have not seen much, really,” he said.
“I do not see much football, but I know he is a good player and if he comes it is because he has had a great last season and I hope he helps the team if he comes.”
Were Mbappe to arrive at the Bernabeu, manager Zinedine Zidane would have to fit him into a system already consisting of Bale, Cristiano Ronaldo and Karim Benzema.
Asked about his fellow two strikers, Bale said: “We spend time together, we feel very comfortable and we have won many things together. It is the coach’s decision how the team has to play and we will do our best.”
The battle over Mbappe has lasted for months, with Arsenal and Real Madrid having had £87m bids rejected by Monaco.
The Ligue 1 champions are determined to keep their star man – in part because Tiemoue Bakayoko and Bernardo Silva have already been reluctantly sold.
Monaco have earned £83m from those two transfers alone and have invested in their squad, with Feyenoord’s Terence Kongolo, Lyon ace Jordy Gaspar and Wolfsburg goalkeeper Diego Benaglio all arriving.
As for Bale, he added to Marca that a proposed move to Manchester United is not something he is considering.
“The truth is that I do not read any of that. Logically I am a British player and I am always linked with a return home,” he said.
“It happened with Beckham, with other Englishmen who came to Spain.
“Nothing new. I am happy playing in Madrid, logically interest is interest, but if there has been nothing concrete, no offer, there is nothing to discuss.”