The Norwegian recently signed a new deal, on reduced wages, to continue at Oslo club Valerenga, where he moved after quitting Parkhead in 2016.
But he's the No.1 choice now to take charge of MLS new boys New York City FC, after they missed out on former Rangers midfielder Giovanni van Bronckhorst, who opted instead to move to Chinese club Guangzhou R&F.
Deila has had strong links with the club's owners, City Football Group, since Deila led Stromsgodset to the Norwegian title when they were also an affiliate club of Manchester City.
And the 44-year-old is strong favourite to replace former head coach Dome Torrent, who left the club in November.
Valerenga general manager Erik Espeseth said: "We do not contribute to speculation in terms of player logistics or coach questions."
If he completes the move, Deila would see a familiar face at the Big Apple club - he signed winger Gary Mackay-Steven from Dundee United for Celtic five years ago.
Deila won two league titles and a League Cup during his time in Glasgow.