The 26-year-old joined Neil Lennon's side in 2010 after previously representing the newly promoted Premier League side.
Reports have suggested the Welshman could be set to return in a £3million deal.
But he moved to quell the speculation and expects to enter talks over a new deal at Celtic Park.
"We still haven't officially spoken to the club at the moment," he said.
"My agent has been away and the club has been pretty busy as well with sorting out new players.
"Hopefully I will be next and sort something out. In the next couple of weeks, if we could sort something out, it would be brilliant."
On the alleged Cardiff transfer, Ledley insisted he had not had any contact from the Cardiff City Stadium and was only focused on Celtic's upcoming UEFA Champions League qualifier against Elfsborg.
He added: "It's just rumours at the moment. There has been nothing official.
"A lot of players want to play in the Premier League and that's why they have done pretty well with their signings so far.
"It does attract people, but at the moment I'm with Celtic and I'm just concentrating on a big week ahead of me."
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