Former Hoops midfielder Paul Hartley reckons the club will have to make a “marquee appointment” in the summer to get fans back on board.
In a conversation with the Celtic Huddle Podcast, the Cove Rangers boss mentioned Roy Keane as a possible candidate, who had a short spell at Parkhead.
“For me, if Celtic are going to go and get a marquee manager, it will probably be someone out of a job,” Hartley said.
“I think the fans have been fed up this season, the criticism the squad’s had, I think they expect a big marquee name in the summer.
Meanwhile, Spanish football expert Guillem Balague has tipped Domenec Torrent for the job.
Torrent is a former assistant to Pep Guardiola and has most recently been in charge of Brazilian giants Flamengo.
Balague tweeted: “@DomeTorrent would be in my eyes a very exciting move. Number two to Pep at Bayern and City, and a great believer in possession based football and in the need to give spectacle to fans."
However, the bookmakers have made John Kennedy the strong favourite. Some outlets have him odds-on favourite to land the job permanently.
Currently interim boss after being part of the coaching staff under Brendan Rodgers and Neil Lennon, the former centre-back won his first match in charge, a tight 1-0 win over Aberdeen at the weekend.
The likelihood is that he will have to lead the club to wins in their next two games, against Dundee United and Rangers, to prevent their rivals from winning the title at Parkhead.