The Scottish Premiership leaders, still hurting from Sunday’s Scottish Cup semi-final defeat by Rangers, say Norwegian Deila is going of his own volition.
Neil Lennon, former manager of Town’s Championship rivals Bolton Wanderers, is being linked with a return to Celtic, where he was in charge between 2010-14.
Other names in the frame include Roy Keane, David Moyes and Malky Mackay, like Lennon, former Celtic players.
But there is a school of thought which says Celtic should follow the lead of Rangers by looking to the Football League.
The Ibrox club have won promotion back to the top flight and made the Scottish Cup final under former Brentford boss Mark Warburton.
And suggested names Celtic should look at include Wagner, Gary Rowett, in charge of Birmingham City, who visit Town on Saturday, Wigan Athletic’s Gary Caldwell, a former Celtic skipper, and Leeds United’s Steve Evans.
Wagner, the former Borussia Dortmund II chief, has certainly made the headlines since taking over as Town’s head coach in November.
The German has introduced full-throttle football, like that played by Liverpool under his close friend Jurgen Klopp, and ensured Championship survival.
Now Town, currently 16th, are looking to push on in 2016-17, when they will have a number of new signings on board.
They include German defenders Chris Loewe and Michael Hefele.
Former US international striker Wagner, 44, is on a 12-month rolling contract at Town.