The Black Cats have tabled a bid for the Scotland international as manager Martin O'Neill attempts to rebuild his pool of frontmen, but the Black Country club's initial response appears to be a stubborn refusal.
Chief executive Jez Moxey told the Wolverhampton Express and Star: "We are not getting drawn on offers for players in or out. Our best players are not for sale; we want to keep them and build the strongest possible team for the season ahead.
"We will do everything we can to retain the players we want to keep and continue to look to strengthen with new signings."
Sunderland boss Martin O'Neill has made 25-year-old Fletcher one of his main targets this summer and, with the start of the new season less than three weeks away, he is keen to make progress.
Wolves' stance is unlikely to have come as a surprise as they attempt to bounce back into the Premier League at the first attempt having suffered relegation at the end of last season.
Meanwhile, Wolves have completed the signing of Mali international Tongo Doumbia on a season-long loan from Rennes.
The 6ft 3in midfielder moves to Molineux with a view to a permanent deal having completed a medical on Friday before joining his new team-mates for training over the weekend.
"I am delighted we have managed to sign Tongo who will bring some more quality to the squad," boss Stale Solbakken told Wolves' official website.
"He also has good experience for a young player and made 26 appearances last season for a top six club in France.
"He is a box-to-box player who can operate in that central role defensively and offensively and as well as being physically strong he is also good in possession.
"We'll have another look at him on Tuesday but there is a chance he will be involved in the game against Shrewsbury."