The La Liga side are reported to have lodged a world-record bid of £85m to tempt Spurs into selling their prized asset this summer.
The 24-year-old became one of Europe’s hottest properties after scoring 21 Premier League goals from midfield last season.
And Kaká, who joined Madrid in 2009, rates Bale as an “amazing player” and would like to see the Wales international at Los Blancos.
“He’s a very, very good player,” said Kaká on Sky Sports News. “If he comes to Madrid he will be welcomed.”
He added: “He’s an amazing player with lots of technical ability, skills and tricks. We will be very happy if he comes.”
On Wednesday, Madrid defender Sergio Ramos also backed the club’s pursuit of the Tottenham star.
“I think the mixing of veteran players as well as young players is a great philosophy.
“Not only as a team but in providing young people for some of us who have been here for so many years.
“Facing up to the challenges, and in that sense, those who are in a position to decide will leave us with our job to do.
“I think they have to work that out with (Real coach) Carlo Ancelotti, they must decide whether they need more players.”