The Motherwell manager spent four years as a player at Celtic in the late 1980s and is a close friend of Strachan. His profile was boosted when he transformed Well from relegation fodder to the third best team in the SPL in his first season in charge. He also made the shortlist for the Scotland job before losing out to George Burley.
Another contender who has a background as a player with Celtic between 1991 and 1995. Mowbray began his managerial career in Scotland with Hibernian and has earned plenty of plaudits south of the border with West Brom. However, the Baggies' relegation from the Premier League means he could be tempted by the east end of Glasgow.
McCarthy's managerial credentials are sky-high just now after guiding Wolves to the Premier League after leading the Championship table for most of the season. Spells at Millwall and Sunderland, as well as the Republic of Ireland, means he has the experience for the Celtic job and two years as a player at Parkhead means he has knowledge of the club.
Coyle has been a revelation at Burnley - following previous spells as manager at Falkirk and St Johnstone - leading the club to England's top flight for the first time in 33 years after triumphing in the Championship play-off final at Wembley on the same day Strachan quit Celtic. He will be relishing the prospect of testing himself in the Premier League but the Celtic job could be a tempting option.
Moyes began his senior playing career at Celtic and has expressed a desire to return to Scotland as a manager one day. However, the Everton boss recently claimed he would be reluctant to leave the Premier League just yet and, having also been tipped as a potential successor to Sir Alex Ferguson at Manchester United, looks set to remain in England for the time being.