Poyet is currently in charge of promotion-chasing Brighton, while McDermott is out of work after leaving Reading last month.
The latter openly spoke about the Yorkshire club during a television interview at the weekend and, while Poyet has not commented, Press Association Sport understands the Uruguayan would consider a return to Elland Road if an approach was made.
The 45-year-old was a popular assistant to Dennis Wise between in 2006 and 2007 and has previously spoken of his love for the club, saying in February last year: "I would love in the future to manage Leeds. I would really like to come back. Probably the timing is not right."
He remains committed to Brighton at present, though, and last month turned down Reading's advances. Albion play Charlton on Tuesday night looking to move into fifth place in the Championship table.
Leeds' owners GFH Capital, who welcomed Warnock's offer to leave the club last night, have placed Neil Redfearn in temporary charge until they can get the man they want.
They have given few clues as to who that is - they have previously stated a preference for a young manager - but McDermott talked up Leeds' credentials when asked about the position and is known to be interested.
Whoever takes the role will inherit a squad Warnock hoped would give him the record eighth promotion he wanted in what he said would be his final job.
He has claimed throughout this season that once promotion was not an option for Leeds he would go and he did so last night, although he believes that had he received better backing in the transfer window, things would have been different.
GFH Capital completed their seven-month takeover of the club in December but business was not as fruitful in January as had been expected, with the sale of 19-goal Luciano Becchio to Norwich the headline transaction.
"I was instrumental in getting them (GFH) on board. They came in a little too late for January but the new manager will get the benefit of that," Warnock said on Sky Sports News this morning.
"They are not really football people but they are aware of the quality we need now.
"We needed two or three forwards and we suggested some but they wanted to come in and see what the club needed - I wanted it instantaneously."