Deila's agent Tore Pedersen was at Celtic Park on Wednesday and it is understood the two sides are close to an agreement.
The 38-year-old, who has been likened to Dortmund boss Jurgen Klopp, remained at home to watch his Stromgodset side drop out of the Norwegian Cup with a shock 4-2 defeat to lower-league side Tromsdalen.
"It's flattering as Celtic are a big club," said the Norwegian, who last season led Stromsgodset to their first domestic title in 42 years.
"I have always said I dream about working abroad one day.
"It's great to be linked to a club like Celtic but I've been in football a long time and nothing is secure in it and I can only talk about things that are concrete."
Celtic chief executive Peter Lawwell expects to be able to make a decision on a new boss in the coming days as he continues his search for a successor to Neil Lennon, who quit last month.