The Stromsgodset manager has jumped to the top of the Scottish champions' wanted list as they step up their efforts to replace Neil Lennon.
It is understood that Celtic have made contact with the 38-year-old Norwegian's current club but a compensation package has yet to be signed off.
However, Deila's agent Tore Pedersen was at Celtic Park on Wednesday and the two sides are not far away from an agreement.
Pedersen's client has remained in Norway as he watched Stromgodset drop out of the Norwegian Cup to lower-league Tromsdalen after a 4-2 defeat.
But Deila - who guided his team to the domestic league title last term - was quoted by several newspapers on Thursday morning responding to the Hoops' interest by saying: "It's flattering as Celtic are a big club.
"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."