The Bhoys' hierarchy are searching for a new boss following the resignation of Neil Lennon after four years at the club.
"We have got a number of excellent candidates, Roy is one of them and we'll see what happens in the next week or two," Lawwell told reporters.
"He's played here, he's a Celtic supporter, he's a first-class guy. As I said we have between five and 10 candidates.
"You just have to do your work properly and hopefully we'll get it done as soon as we can. As soon as we do that we will let our supporters know."
Keane is currently assistant coach to O'Neill in the Ireland setup.