Newspaper reports on Monday claimed the Wales midfielder, who left his hometown club for Parkhead three years ago, is a target for Malky Mackay ahead of City's debut season in the Premier League.
But Ledley says it would be "brilliant" to agree a new contract with the Scottish champions as he prepares to enter the final season of his current deal.
"It's just rumours at the moment," he said when asked about the Cardiff link. "There has been nothing official.
"A lot of players want to play in the Premier League. It does attract people, but at the moment I'm with Celtic and I'm just concentrating on a big week ahead of me.
"We still haven't actually spoken to the club (about a new contract). 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."
Ledley has been troubled by injuries in pre-season but featured in a weekend friendly against Borussia Monchengladbach and hopes to be included in the squad for Wednesday's Champions League qualifier against Elfsborg.
He said: "I'm obviously still not match fit, but it would be brilliant if I could get involved. I'm going to be a little bit rusty as I haven't played much, but if I am starting I'll give it my all."
Ajax winger Derk Boerrigter is expected to sign for Celtic this week, and Ledley said: "Bringing the Dutch guy in from Ajax proves we are going in the right direction.
"If the deal is done, I look forward to working with him and he will be a big boost to the squad."