United announced Evans' protracted departure on Tuesday night, saying they wanted to go in a different direction to the Scot who had claimed he would be given a new deal beyond the end of this month if he kept the club in the Championship.
That contract was not forthcoming, though, and after a three-week wait to learn his fate - a time during which owner Massimo Cellino interviewed other people for his role - he was let go.
Monk is not thought to be one of those Cellino met while Evans was in place - MK Dons' Karl Robinson was one while an approach was made for Bristol Rovers' Darrell Clarke - but he now looks to be the front-runner, with some reports suggesting talks have begun.
Press Association Sport understands Monk is the leading candidate Cellino is now focussing on to replace Evans, with the 37-year-old out of work since leaving Swansea in December last year.
Prior to that he had been upgraded from player-manager to the outright boss, guiding the Swans to eighth place in the Premier League in his only full season in charge, 2014-15.
Should he choose to take on the Leeds job then it will raise the eyebrows of many, given Cellino's propensity for dispensing of managers.
Evans was the sixth to lose his job under the Italian's two-year stewardship. Brian McDermott, David Hockaday, Darko Milanic, Neil Redfearn and Uwe Rosler also bit the dust, and it will require a brave candidate to take on Cellino.
Away from his firing record, he has also made the bold pledge to refund supporters either 25 per cent or 50 per cent of their season ticket outlay if Leeds fail to make the play-offs next season - a burden the new manager must carry.
For some time Evans had believed that would be him, only to be told by club secretary Stuart Hayton - on behalf of Cellino - that his time was up.
"It is with great sadness that I have learned my contract will not be renewed," he said. "It perhaps became obvious to everyone in football that the decision not to renew my contract had been reached many weeks ago, but at all times I have kept my dignity as a matter of respect for the history and tradition of this football club."
As Cellino met Robinson and approached Clarke, it made for an embarrassing situation for Evans and did little to endear Cellino to the Leeds support.
He is currently the subject of a Football Association charge for an alleged breach of its agent regulations, while he has also served a Football League ban for tax evasion.
His ownership has come under heavy criticism from fans, with the 'Time To Go Massimo' protest group particularly vociferous.
A fortnight ago the Italian said he wanted to sell the club - not for the first time - although the appointment of a name like Monk would be received well.
There was no comment from Leeds on Wednesday.