The Irishman has been linked with a return to Parkhead.
The 44-year-old is one of a host of names being linked with the role at Parkhead, alongside the likes of Paul Lambert, David Moyes and Brendan Rodgers.
However, Keane, who enjoyed a brief playing career with the Hoops, is currently Martin O'Neill's assistant in the Republic of Ireland set-up and with Euro 2016 just over a month away, he insists his focus is solely on that competition for the moment.
But the legendary midfielder, who has previously managed Sunderland and Ipswich Town, with contrasting success, says that he would not even consider returning to Celtic in a managerial capacity unless the board's hierarchy approach him.
"The only time you think you might be interested in a job, or the only time you know, is if you're asked," Keane told ESPN, via Soccerway.
"So this idea of speculation about other clubs ... there's always club jobs coming up.
"There'll be club jobs coming up over the next few weeks. But until someone asks you the question, 'would you take that job?', there's no question to answer."
The Irishman, a Champions League winner with Manchester United in 1999, added: "And at the moment, my focus is working with Martin and all the players and staff and making sure that we go to the Euros and make Ireland proud. Everything else will fall into place after that."
Celtic chief executive Peter Lawwell has a fairly hit and miss record when it comes to appointments, as Keane does in management it must be said.
He guided Sunderland to Premier League promotion in 2007, before resigning in December 2008 after keeping them up in their first season back, but his stint at Portman Road was not so successful and he was sacked in January 2011, less than two years after getting the job.