He told reporters: “There is only one thing that needs to be sorted out here and that is me sitting down with the owners when they are ready to talk about me being at West Ham and nowhere else.
“Until that is resolved we won’t know which way we are both going forward. That is the only thing that is to be sorted, to sit down and sort it out.”
Reports of Allardyce taking over at the Stadium of Light next term have surfaced, of course, because the 60-year-old's contract with the Hammers is up at the end of the season and has still not been renewed.
The West Ham boss is third-favourite with bookmakers, according to sports betting website Oddschecker, to take charge of the Black Cats, who have hired Dick Advocaat as manager until the conclusion of the current campaign.
But, despite his coyness, Allardyce is the perfect man for the Sunderland job next term - and he may just know it.
West Ham and Big Sam have had their time together: the desire for change is palpable. The fans and owners at Upton Park appear to want a little more than Allardyce can offer: expansive football and ambition.
What Allardyce is brilliant at, however, is exactly what Sunderland need right now.
The 60-year-old specialises (his side's poor recent form aside) in defensive solidity and making a club stable within the Premier League. That's what the struggling Black Cats desperately require and nothing more.
Allardyce is, too, a former Sunderland player (and his unsuccessful stint as Newcastle manager may also help!), while he would still be suitable should the Wearside outfit go down: he took West Ham up from the Championship when he arrived in east London.
He can succeed in the transfer market with financial limitations and he will do a better job than anyone of making sure Sunderland stay up (or go up).
There may be a question mark over whether Allardyce will work with a director of football but, should an agreement be arranged, there is no better candidate ahead of next season - Advocaat included.