The 32-year-old attacker will soon become a free agent when his Real Madrid contract expires on June 30.
According to the PA news agency, via the Evening Standard, Cardiff's training complex is shared with the FA of Wales' medical staff and Bale was seen at the club's training ground on Wednesday to undergo physiotherapy.
The report adds that Bale held an 'informal' conversation with Bluebirds boss Steve Morison, and the attacker is still keeping his options open before deciding on his future.
Bale would be required to take a significant wage cut should he opt to join Cardiff, having previously earned around £600,000 per week during his time at Real Madrid.
The 105-cap Wales international will look to join a new club this summer and play regularly before representing his country at the 2022 World Cup in Qatar later this year.