HITC Sport understands that Vincent Tan is prepared to sanction a move, but a deal may have to wait until January.
Cardiff were one of a number of club interested in landing the Welsh midfielder towards the end of the summer transfer window, but he remained at Selhurst Park.
With record signing Yohan Cabaye forming an outstanding partnership in central midfield with James McArthur, and the likes of Yannick Bolasie, Wilfred Zaha, Jason Puncheon and Bacary Sako filling the wide roles – Ledley’s role could become limited over the coming months.
He has started just one game so far this season, although he has been injured – but his hometown club Cardiff would relish the opportunity to bring him back to the Welsh capital.
The Bluebirds are pushing for promotion back to the Premier League and owner Vincent Tan is understood to be willing to fund the move as it would require a big outlay for the Championship club – although they may well have to wait until January to push through a deal, as Palace cannot replace him until the transfer window re-opens.