Sunderland have confirmed that manager Sam Allardyce was given permission to speak to the Football Association regarding the England vacancy, but are unhappy with the "disruption" that the discussions have caused.
It was recently reported that the 61-year-old was interviewed for the job at the home of FA vice-chairman David Gill on Tuesday afternoon.
A three-man panel has been tasked with finding the next England boss following Roy Hodgson's resignation, which was confirmed shortly after the Three Lions' last-16 exit at Euro 2016 in June.
Sunderland released a statement this morning confirming that talks between the FA and Allardyce have taken place, but they have described the speculation as "extremely damaging" and seek a "swift resolution".
The statement via the club's official website read: "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. 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."
Allardyce was appointed manager of the Black Cats just nine months ago, and helped the club retain their Premier League status.