The former Celtic boss is approaching his second anniversary as boss of the Oslo club - his first job since he left Parkhead in 2016.
But their 2-0 defeat at another of his former clubs, Stromsgodset, has pushed Deila to the edge, after just one win in seven games.
They are now languishing in eighth place in the Norwegian top flight and the 43-year-old has hinted he has lost patience with his players and the job.
He said: “It must be something I am doing wrong because is not good enough. It is my responsibility.
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“I am going to take a long hard look at myself. I am the leader of this club and I have to look in the mirror.
“If I cannot influence the players then perhaps I have to start looking at myself.
“I’m sorry for the fans who have had to watch this, but it’s not good enough. I thought last week’s defeat to Kristiansund was as bad as it could get, but this was actually even worse.
“I am going to take time and reflect on this. Something has gone very wrong.”
Deila won a Norwegian title and Cup with Stromsgodset, before lifting two titles and a League Cup with the Hoops.