Norwegian coach headed to Celtic Park
While the likes of Roy Keane, Paolo Di Canio and Michael Laudrup have all been mentioned as possible replacements for Neil Lennon, Deila, who led unfashionable Norwegian club Stromsgodset to the 2013 Tippeligaen title, has jumped to the head of the queue.
The 38-year-old, who also won the 2010 Norwegian Cup with Stromsgodset, has flown to Glasgow to meet with Celtic's owners.
"It's flattering as Celtic are a big club," Deila said.
"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."
Stromsgodset won their first league title in the Norwegian top tier in 43 years - and just their second ever - when Deila led them to victory last year.
The club from the town of Drammen, less than 50 kilometres south-west of Oslo, only returned to the Tippeligaen in 2007 after five seasons in the second tier.
In their first five seasons back in the top flight, Stromsgodset generally battled relegation or finished mid-table.
But after winning the Norwegian Cup in 2010, Stromsgodset followed that up with a second-place finish in 2012 and last year's league triumph.
While it is widely expected Deila will leave if offered the job at Celtic, Stromsgodset chairman Tom Saxegaard indicated the Norwegian club will fight any advances by the Scottish Premiership outfit.
"We are going to play in the (UEFA) Champions League this year and, obviously, we want to keep him," Saxegaard said.
"He's our manager and is under contract with us for two-and-a-half-years. We really think he can get to the very top."