Here, the PA news agency looks at possible replacements for the Northern Irishman.
The Scotland boss has emerged as one of the favourites in recent days even though he has declared he will not leave his job before leading his country into their first major tournament in 23 years this summer. Celtic may be prepared to wait until after the delayed Euro 2020 if they believe the former West Brom and Reading boss can have the same impact in Glasgow as he did when twice leading Kilmarnock to club-record points tallies.
One of the most candid characters in football, the former Republic of Ireland skipper is best known for his hugely successful time at Manchester United but he had a short spell at Parkhead at the end of his career. Keane bossed Sunderland and Ipswich before becoming assistant at Republic of Ireland, Aston Villa and Nottingham Forest. Now a pundit, Keane, 49, declared an approach by Celtic “failed to rock my boat” in 2014.
It has long been thought that the former Celtic defender is a future Celtic manager. The 37-year-old has been at Parkhead for years in various roles. He was appointed first-team coach under Ronny Deila and carried on under Brendan Rodgers and was promoted to assistant manager when Lennon replaced his fellow Northern Irishman in February 2019. However, as part of the Lennon regime, he may have to depart and return another day.
The former Northern Ireland international is currently boss of Championship side Stoke. After a playing career which included spells at Dundee United and Hibernian, he cut his managerial teeth at Brechin and Shamrock Rovers. As Northern Ireland boss, he qualified the country for their first ever European Championships, Euro 2016 in France. In 2018, the 51-year-old turned down the chance to become manager of Scotland but maybe the challenge at Celtic could tempt him.
Many may think it is the destiny of the former Celtic and Sweden striker to end up back at Parkhead as manager. However, the 49-year-old, who became a Hoops hero when played for Celtic between 1997 and 2004, has had an indifferent time as either assistant or manager at several clubs such as Landskrona, Hogaborgs, Falkenbergs, Helsingborgs and Angelholms. Larsson is still much sought after however and in August he joined Ronald Koeman’s coaching staff at another former club, Barcelona.
The 43-year-old former Bournemouth manager has previously been a clear favourite of the bookmakers and remains so with many fans on social media. Howe spent most of his playing career with the Cherries and started out his managerial career with the south coast club in 2008. After a brief spell as manager at Burnley, Howe returned to Bournemouth and led them to two promotions in three seasons, taking them to the Premier League for the first time. Bournemouth were relegated to the Championship in 2020, and Howe left the club by mutual consent in August but his reputation remains intact.
The former Alloa and St Mirren boss has rebuilt his reputation at Hibernian after a brief spell at Sunderland ended following failure in the League One play-offs. Ross achieved promotion with Saints and has Hibs in pole position to claim third spot in the Premiership. The 44-year-old won an influential admirer in Brendan Rodgers when facing Celtic with his first two clubs.