Ledley's current deal expires at the end of the season and there had been suggestions Cardiff could cash in on the Wales international during the transfer window.
Hull and Wolves were linked with the midfielder, but no bids came in to offer Ledley a move to the Premier League and with the transfer window now closed, Cardiff have moved to tie the 22-year-old down to a new long-term deal.
Ledley suggested last week that he would be willing to extend his stay at the club and Ridsdale is now waiting for the player's response.
"We have put a new contract before Joe and he is considering it," said Ridsdale in the Western Mail
"We believe it is a good deal and the ball is now in Joe's court."
Meanwhile, Ridsdale is confident that Bluebirds boss Dave Jones has now assembled a squad capable of challenging for promotion to the top flight.
He added: "I believe in the seven players we have brought in we have seven quality players.
"I am delighted with the rebuilding work myself and Dave have carried out to the squad during the course of the summer.
"I feel now we have cover across every position on the pitch and that is exactly what we were aiming for.
"I believe we have a squad assembled now which can have a successful campaign in the Championship."
Coca Cola Ch'ship 09/10 Win Outright: Cardiff 11/1