Aberdeen closed the gap at the top of the table to just three points after they clinched a victory when the pair met on Wednesday.
The Norwegian is under serious pressure following the Hoops' defeat to second place Aberdeen on Wednesday, and Deila explained that if the Dons go on to clinch the league crown, then he would be willing to step aside at Parkhead.
When asked whether missing out on the league title would persuade him to resign, Deila responded (via Record) :"It speaks for itself - my future is over here. I wouldn't see any reason to continue then, you know. Then I haven't done my job, of course."
The defeat at Pittodrie meant that the gap at the top of the table was cut to just three points, and while the lead - as well as the vastly superior goal difference - means that the Bhoys are still favourites to go on and lift the trophy at the end of the season, the club's last two results appear to have forced Deila to take a serious look at his own future.
The surprise defeat to Ross County in the Scottish League Cup semi-final, as well as the failure in Europe earlier in the season, appears to suggest that Celtic have not progressed as much as they would have liked since he arrived at the club, meaning that a third consecutive defeat would surely see the pressure on Deila reach an unimaginable level, as they come up against minnows East Kilbride in the Scottish Cup.
If they come through that game unscathed, Deila will still surely be under the same pressure he finds himself now. And while winning the league title may the difference between him staying or going in his own mind, it still seems unlikely that Celtic supporters will be content with winnng the Premiership crown if they manage it by just limping over the line, given the dominance they have enjoyed in previous years.
It appears that only a nearly flawless run of form that results in them winning the league in emphatic style will be enough to perhaps relieve some of the growing pressure on Deila's shoulders.