The Real Madrid legend has offered £40m to Cardiff owner Vincent Tan, says The Times.
Tan is set to reject the proposal, though is open to negotiations.
Bale is heading a US-based group in their push to buy the Championship club.
"We are interested in getting Cardiff," Bale said last month. "It's my home club, it's where I grew up and my uncle (Chris Pike) used to play for them. To be involved with an ownership group would be a dream come true.
"It's a club close to my heart. It's where I grew up and I would love to be able to be a part of growing Cardiff and taking it to the Premier League where it belongs.
"I know how amazing the Welsh fans and Cardiff fans are. It would be amazing to try and do something together.
"We are trying to engage with Cardiff and more news will come out on that in the future but hopefully we can get something done."