The 61-year-old held talks with the Football Association on Tuesday after leaving the club's pre-season training camp in Austria ostensibly to continue his pursuit of summer transfer targets.
However, after the Black Cats confirmed on Wednesday that he had been given permission to meet the FA's representatives for what were supposed to be confidential talks, he is now back in harness on Wearside.
Allardyce is understood to be one of a series of potential candidates due to hold discussions with FA technical director Dan Ashworth, chief executive Martin Glenn and vice-chairman David Gill with Hull's Steve Bruce, Bournemouth's Eddie Howe and Unites States head coach Jurgen Klinsmann also reportedly in their sights.
But whatever happens, Sunderland are hoping for a swift conclusion to the matter as they contemplate the prospect of having to find a ninth permanent manager inside eight years, something they are desperate to avoid after believing they had struck gold when they appointed their current manager in October last year.
A club statement said: "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."
The former Bolton, Blackburn and West Ham boss, who was overlooked for the England job a decade ago, has supporters in high places and has received the backing of new Celtic manager Brendan Rodgers.
Rodgers told talkSPORT: "I see they are linked with Big Sam, and you wouldn't go too far wrong with Big Sam because in my meetings with him over the years, I have spoken with him and he's a very intelligent man, very detailed in is approach. He knows what he wants out of the game.
"He gets labelled a wee bit with this style of football, how he wants to play, but I haven't seen that so much in recent years."