Stewart has another year left on his deal at the Stadium of Light.
Sunderland head coach Alex Neil has consistently stressed that the immediate focus has to be on securing a play-off spot and not contract talks, at this stage.
Neil says he has not made any plans beyond the end of the regular season, insisting that the club cannot afford to look beyond the next game in their bid to secure a play-off spot.
Neil confirmed recently that there has therefore not been any discussions with any of the club's playing staff about their futures beyond the end of the season.
The Black Cats have seven senior players out of contract at the end of the campaign: Lee Burge, Lynden Gooch, Aiden McGeady, Arbenit Xhemajli, Patrick Roberts, Bailey Wright & Jordan Willis.
The future of the club's five loanees is also uncertain and likely to be dependent at least in part on how Sunderland's promotion push ends.
Neil said: “There is none of those discussions taking place with any player.
"Everybody has been spoken to when I walked in the building and I’ve told them all, whatever your agenda looks like, whatever your dynamics are, park it.
“Because our sole focus at the moment is to try and finish the season as well as we can. Once we get to the end of the season, if we are successful in what we are trying to achieve, every single person will be in a better place to renegotiate a contract, move onto another club if that is what their desire is. Potentially stay here if that is what their desire is. All of that will be in a better place if we are successful.
“If we’re not successful, then that’s when that becomes more difficult. So let’s park that to one side and focus on the job at hand."
Sunderland host Shrewsbury at the Stadium of Light on Good Friday.