The 22-year-old, who has been linked with the likes of Everton, Stoke and Hull in recent times, is out of contract at the end of the season.
Ledley has played over 200 games for his hometown club, who he joined as a nine-year-old.
The Wales international admits he has been in contract negotiations with Cardiff and is hoping to come resolve his future in the near future.
He told BBC Sport Wales: "Hopefully we'll try and sort something out in the next couple of days or weeks. If the contract is good enough for me and what I think I deserve then I'll sign it.
"So it's down to the club to put something in front of me and if it's good enough then I'll sign it."