The Wales international, a product of Cardiff's youth academy, departed his boyhood club for Glasgow in 2010, six years after his senior debut.
The Bluebirds are favourites for promotion from the Championship this season, sitting seven points clear at the top of the table, and are thought to be targeting Ledley as they eye Premier League football next term.
Ledley says Wales international team-mate Aaron Ramsey has informed him of the rumours but while he stopped short of ruling out a return, he expects to be at Celtic next season.
He told the Daily Record: "Aaron Ramsey actually told me about the story that Cardiff City wanted me back if they go the Premiership.
"They are certainly looking good for promotion. They are clear at the top and have an excellent squad. (Manager) Malky Mackay has done a fantastic job.
"I haven't heard anything about a move at the moment so I can only assume it's just paper talk.
"I still have another year with Celtic and I'm happy with the way things have gone as it has been a brilliant season.
"You never know in football, anything can happen, but I'm happy here and am looking forward to next season.
"Everyone knows it's been a good season for Celtic and hopefully I'll be there next season."
Ledley says he is yet to engage in talks with Celtic over a contract extension but expects discussions once the campaign is over.
"There is nothing new in terms of talking about a new deal. I've still got another year left so there's plenty of time," he said.
"I think we'll wait until the end of the season. Hopefully I can continue at Celtic as it's a fantastic club and I really enjoy it and they've been brilliant with me."