The Gateshead manager is now the overwhelming favourite with bookmakers for the job.
Elliot is as short as 1/4 for the job with Betano, having previously been Evens and then 1/2.
United are seeking a successor to manager Paul Simpson, with the recruitment of a new head coach as well as a sporting director now at a more advanced stage.
The appointment of the latter is expected to be announced first though there have not yet been any firm indications on timescales from Brunton Park.
Elliot was named Vanarama National League manager of the month for August after guiding unbeaten Gateshead to the top of the table.
Speculation linking the former Newcastle United goalkeeper to the Blues has been persistent as the recruitment and interview process has progressed at United.
Ryan Lowe, the former Preston North End boss, is now a more distant second favourite at 8/1 with others remaining on the bookies’ shortlist including ex-Manchester City Under-21 boss Brian Barry-Murphy, former Wycombe Wanderers chief Gareth Ainsworth and ex-Barrow manager Pete Wild.
Elliot has attracted plaudits both for Gateshead’s impressive results and their attractive style of play in non-league’s top tier.
United saw evidence of that in pre-season when they were outplayed by the north east club in a 2-0 friendly defeat at the International Stadium.
The Heed have since chalked up five wins and two draws from their seven league games so far.
Elliot has been in permanent charge since June, having been interim manager since last October after previous boss Mike Williamson’s departure to MK Dons.
The former Charlton Athletic No1 was initially technical director at Gateshead from August 2022.
United owner Tom Piatak, after Simpson’s departure, said the Blues wanted the next boss to oversee a certain “front-foot” style of play.
Piatak also said the Blues were unlikely to gamble on a complete rookie in the hot seat. He told the News & Star: “We need someone with experience, and we’re not going to be taking somebody that’s unproven, that has absolutely no experience at all, and throw them into the EFL and say, ‘Let’s go, let’s hit the ground running’.”
Caretakers Steven Rudd, Mark Birch and Jamie Devitt remain in interim charge as they prepare the team for this weekend’s home League Two clash with Fleetwood Town – their third game at the helm.