Paul McStay is the latest former Celtic player to back Neil Lennon for the manager's post at Parkhead.
"I'd be very comfortable with Neil getting the job," McStay, who won three league titles in his 16 years with the club, told BBC Scotland.
"Anybody that manages Celtic needs something special if they're going to be successful and it helps that he understands the place already.
"Experience is probably the only thing that would affect his chances."
Lennon stepped into the manager's role on a temporary basis when Tony Mowbray was sacked in March and won all of the eight league matches that he oversaw.
The only black mark in his short tenure was a shock defeat by First Division Ross County in the Scottish Cup semi-final.
"I'm sure there will be a few people chapping the door because Celtic is one of the biggest clubs in the world but Neil is in the driving seat and he should be the front runner," added McStay, who made 76 appearances for Scotland.
"Over a short period of time he has shown he can bring success to the club with a lot of good wins and if he was given more time to continue, maybe more success would follow.
"I think the earlier a decision is made the better for the players and probably Neil as well.
"It depends on the criteria set out by the board, whether it's experience they want or if they are happy to allow Neil to continue what has been a successful role.
"He's taken a team who were maybe down on their luck and self confidence and turned it round.
"I know there was a sticky start with the Ross County game but I think that shows you what Neil is all about because he took those same players and made sure that did not happen again.
"Whatever he's done, with his man-management and his tactics, he's got things right. Between that cup game and the end of the season, things went very well."
Meanwhile, Pat McCourt is targeting more starts for Celtic next season after his three goals from 15 appearances this term.
"It's been alright," the midfielder told the club website, reflecting on a campaign without silverware at Celtic Park.
"I managed to make my full debut and went on to make a few starts and get a few goals. So it's not been bad but it's not been great either, although it's been an improvement on my first season.
"Obviously making my full debut, scoring and picking up the man of the match were all personal highlights. It was a season where there weren't too many highlights for the club though, as it was a poor season by Celtic's standards.
"I was hoping to do establish myself this year. Obviously it hasn't quite happened. There have been a few personal highlights, but on the whole I haven't played as I would have liked. So I'm looking forward to a break now and see what happens for next year."
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