Allardyce's appointment is set to be ratified after a meeting of the Football Association Board on Thursday, leaving the Black Cats without a manager just over three weeks before their opening fixture of the 2016/17 Premier League season.
Sunderland have not responded well to Wednesday night's reports that Allardyce's exit was immanent, releasing a statement expressing their disappointment and frustration.
"Naturally we are aware of the intense media speculation this evening," the statement read.
"However, at the present time Sam Allardyce remains Sunderland manager.
"We share in the anger and frustration of our supporters and would like to assure them that we are working to conclude the matter in the best interests of Sunderland AFC."
The focus has quickly changed to who will replace Allardyce, with former Everton and Manchester United boss Moyes believed to be heading the field of potential candidates.
Moyes has been without a post since November 2015 when he was sacked by La Liga outfit Real Sociedad after a year in charge.