However, Lawwell was keen to stress that, at this stage, Keane remains just one of “a number of excellent candidates”.
Republic of Ireland manager Martin O’Neill – formerly a highly successful Celtic manager himself – revealed earlier this week that Keane had held informal discussions with the club’s majority shareholder Dermot Desmond about the job vacated by Neil Lennon earlier this month.
Now Lawwell has confirmed the 42-year-old former Manchester United skipper – who ended his playing career at Parkhead – is on a shortlist of “between five and ten” candidates the Celtic board is now assessing.
Lawwell said: “We are looking at a number of exceptional candidates and we’re going through a process. Hopefully it won’t take too long.
“Clearly we want to do it as soon as we possibly can but these things you just can’t put a time on.
“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.
“He’s played here, he’s a Celtic supporter, he’s a first-class guy – like the others are. As I said, we have between five and ten 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.
“You don’t want to get it wrong by going too fast, you need to take your time and make sure you get the right guy.”
Despite Lawwell’s claims that Keane is just one of a number of candidates for the job, several bookmakers have now suspended betting on the identity of Celtic’s next manager.
Keane himself was on the training pitch with the Republic players in Malahide yesterday morning and O’Neill said there had been no fresh developments since news of Celtic’s interest in Keane surfaced.
O’Neill said: “No, nothing else. There’s nothing else to tell you. I don’t think anything is going to happen anyway until the weekend.”
He confirmed that Keane was due fly to London with the rest of the Republic party yesterday afternoon, ahead of this evening’s friendly against Italy at Craven Cottage.
Keane’s spell as a Celtic player took place under the management of Gordon Strachan in the latter half of the 2005-06 season after bringing down the curtain on a lengthy and enormously successful United career.
After retiring as a player, he went on to manage Sunderland, hauling them from the lower reaches of the Championship into England’s top flight. However, the club struggled in the Premier League under Keane’s management and he left in 2008.
A spell in charge of Ipswich Town followed, but he was unable to kick-start his managerial career at Portman Road and was dismissed in 2011 after 20 months in the job.
In addition to his duties as O’Neill’s assistant, Keane continues to serve as a high-profile football pundit.