The Wales international left his hometown club for Parkhead three years ago but has been linked with a return since the Bluebirds sealed promotion to the Premier League.
However, when asked by reporters about the Cardiff links, Ledley replied: "It's just rumours at the moment. There has been nothing official.
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"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."
The 26-year-old has been hampered by injury during pre-season but made his return to action in Celtic's 2-1 defeat to Borussia Monchengladbach on Saturday.
And Ledley is now hoping to be included in Neil Lennon's squad for Wednesday's Champions League qualifier against Elfsborg at Celtic Park.
"I'm obviously still not match fit but it would be brilliant if I could get involved," he added. "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."