As a result, Telegraph Sport understands the club will make tentative enquiries, through intermediaries, to discover whether former Everton and Manchester United manager David Moyes would be interested in replacing Allardyce, who is likely to recommend the Scot if he does leave.

Given Moyes has been out of work since he was sacked by Real Sociedad in November last year, he is expected to welcome the approach. Other names under consideration are Burnley boss Sean Dyche, while former Manchester United star Ryan Giggs would be another contender, as he looks to take on his first management role since leaving Old Trafford earlier this month.

Interestingly, Sir Alex Ferguson, who encouraged Giggs to leave Manchester United following the appointment of Jose Mourinho as manager, has often spoken of his admiration for Sunderland and welcomed Roy Keane’s decision to become their manager at this start of his coaching career.

Sunderland, though, are currently stuck in limbo and although they are worried about losing their manager, they do not believe it is forgone conclusion Allardyce will be appointed by the FA.

Allardyce was formally interviewed for the job on Tuesday, but Sunderland have been informed the FA are determined to “go through a proper process of elimination.”

As a result, they now expect Allardyce to focus on club matters and have been told he is working to secure their first signing of the summer, despite leaving their training camp in Austria to speak to the FA.

The Black Cats were urged by the FA to keep their approach for Allardyce confidential, but Sunderland released a statement confirming the game’s governing body had formally requested to speak to the 61-year-old after he was photographed leaving the house of FA vice-chairman David Gill.

“The Football Association contacted Sunderland AFC to seek permission to speak with our manager as part of what was supposed to be a confidential discussion process with potential candidates for the position of England manager,” the statement read.

“At Sam Allardyce’s request, we agreed to this. Sam is very much key to our plans. After what was an extremely challenging season, we are keen to see a period of stability, both on and off the field, and we want him to remain as manager of our football club.

“The ongoing speculation over Sam’s position is extremely damaging to Sunderland AFC, particularly at this crucial time of the season and we urge the FA to respect the disruption that this process is causing and bring about a swift resolution to the matter.”

Sunderland are finding it difficult to sign players because of the uncertainty surrounding their manager, and privately fear they will be waiting for at least another week to learn whether Allardyce is staying or not.

Telegraph Sport understands the FA still intend to discuss the job with other interested parties, including Bournemouth manager Eddie Howe and Hull City boss Steve Bruce, although neither have had any direct contact with them.

It is also thought Arsenal manager Arsene Wenger remains in the FA’s thoughts and they could still be attracted to the Frenchman if they are assured he will take up the role when his contract with the Gunners expires in 12-month’s time.

Allardyce, though, appears to be the overwhelming favourite and has heavyweight support in the shape of Ferguson, as well as the head of the League Managers’ Association Richard Bevan.