Reports on Monday suggest the Bluebirds could be set to make a £3million bid to bring the Wales international back to the club he quit for the Hoops in 2010.
Ledley admits the prospect of playing in the Premier League is a big attraction for some players but insists his focus is on the Scottish champions.
He said: "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."
Ledley is in the final year of his Celtic deal and hopes to begin contract talks in the coming weeks.
He said: "We still haven't actually spoken to the club at the moment.
"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.
"At the moment I'm just concentrating on qualifying for Europe and doing brilliantly for the club and playing well."
Ledley has been hampered by injury during pre-season but made his return to action in Saturday's friendly defeat to Borussia Monchengladbach.
And he now hopes to have some part to play in Wednesday's Champions League qualifier against Elfsborg at Celtic Park.
Ledley said: "My fitness is getting there. I played 30 minutes on Saturday, which was a big bonus for me.
"I'm obviously still not match fit because I've only played 30 minutes so far but hopefully I will be in the squad for Wednesday.
"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."
Celtic reached the last 16 last season and Ledley insists qualification for the group stages, at least, is the target this time around as well.
He said: "It's massive and can kick-start our season as well. It's one of the best competitions to be in and we know how difficult it is.
"Last season it was very difficult to qualify and it will be the same this year. We just need to give 100 per cent and keep a clean sheet and you never know."
Meanwhile, Ledley says he would welcome the arrival of Dutchman Derk Boerrigter after Celtic were linked with the Ajax winger.
He 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."