Indeed, the Norwegian has been under pressure all season after a dismal European showing and a Scottish League Cup semi-final exit.
But the Celtic boss's position has taken a big step for the worse after Sunday afternoon's Scottish Cup exit, when the Bhoys lost to Rangers on penalties.
Deila may well find himself leaving the Hoops this summer (or earlier) and attention will then turn to his replacement.
Right now, sports betting website Oddschecker list Moyes as the favourite to succeed the Celtic coach, with odds of 1/2. Lennon is next in the pecking order at 3/1.
The former Liverpool boss is priced at 14/1 and 16/1 with bookmakers to take over at Celtic, while Malky Mackay, Roy Keane and Henrik Larsson can be found at similar odds.
Celtic fans - would you be happy with any of the candidates listed above?