However, Keane, who is currently the assistant manager with the Republic of Ireland and a pundit for ITV, has insisted that he wouldn't be able to take on a third job.
The 42-year-old told Sky Sports News: "I've got a job. I've got two jobs - I can't have another one.
"They are a brilliant club, an absolutely fantastic football club, one of the best in the world. But I have got a job."
Keane played 13 games for Celtic at the end of his playing career.