Bale has been strongly linked with a free transfer to his hometown team following the end of his turbulent nine-year spell in Madrid.
The 32-year-old forward, once the world’s most expensive player, is reported to be considering the pros and cons of joining the Bluebirds before playing for Wales at the World Cup in Qatar in November.
His representatives confirmed to BBC Sport Wales that they are in negotiations with Cardiff chairman Mehmet Dalman.
Bale, a five-time Champions League winner, has several options on the table with MLS teams, his former club Tottenham and Newcastle all mooted as possible destinations.
But he fuelled speculation that he might prefer Cardiff by saying the level of football he plays before the World Cup will not be a determining factor.
Speaking while on international duty with Wales last week, Bale said: “I don’t really know if the standard makes too much of a difference. A football game is a football game.
“I need time to think what’s the best move for me, my family, my kids, and hopefully we’ll sort that over the summer. I have options.”
Bale, who has family in Cardiff, earned around £600,000 ($736,000) per week at Real and would have to take a significant wage cut to sign for Steve Morison’s side.
But his agent Jonathan Barnett said in a recent interview that “what Gareth does next is not about money”.
The sight of Bale at Cardiff’s training ground on Wednesday led some fans to claim he was about to complete the switch to the Bluebirds.
But Cardiff share the facilities with the Football Association of Wales’ medical staff and it is understood Bale was there to undertake physio work.