The former Reading boss was the early favourite to take the role after Neil Warnock's departure but this weeksaw ex-Chelsea chief Roberto Di Matteo heavily backed to move to the head of the market.
Former Leeds defender Dominic Matteo came into the reckoning when cut from 66/1 to 7/1 but it now loos likely McDermott will be given the nod at Elland Road.
There was a gamble on McDermott on Wednesday evening and betting was suspended by Sky Bet as the 52-year-old was supported to as short as 1/7.
The potential appointment would mean there is a Brian McDermott in charge of both Leeds' football and rugby league clubs - with the other Brian already the Leeds Rhinos chief.
Paul Wiggins of Sky Bet said on Thursday: "We started to see a steady stream of business for Brian McDermott at just after 1800 BST yesterday evening.
"Whatever price we went to was backed by a different account which is the usual sign that a possible appointment is imminent. We suspended betting after McDermott reached 1/7 and was still being supported.
"This plunge on McDermott comes after decent support earlier in the week for Dominic Matteo so maybe a coaching role beckons for him in a new set up?"
A brief statement from the club hinted that an appointment was close but did not name names.
It read: "The process of appointing a permanent replacement for Neil Warnock has progressed significantly this week and when all matters are finalised we will be in a position to make a formal announcement.
"Neil Redfearn will remain as caretaker manager until such time when an appointment is made, and he is being kept informed of the situation by the club's board."