Brazilian midfielder Fernandinho has confirmed he wants to join Manchester City.
Juventus sporting director Beppe Marotta says the club are keen to bring in Manchester City star Carlos Tevez.
The Black Cats have tabled a bid for the Scotland international as manager Martin O'Neill attempts to rebuild his pool of forwards, 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 Barclays Premier League at the first attempt having suffered relegation at the end of last season.
However, it may be that the initial exchange is just the preamble for further negotiation as the Black Cats test new manager Stale Solbakken's resolve to retain the player.
O'Neill's need is pressing - the departures of Asamoah Gyan and loan signing Nicklas Bendtner have left him short of senior strikers with Fraizer Campbell, Ji Dong-won, Connor Wickham and Ryan Noble comprising his current stable.
Fletcher certainly fits the bill having scored 30 Premier League goals in three tough top-flight seasons with Burnley and Wolves.
However, even if his current employers do decide to cash in on one of their more saleable assets, the Wearsiders are unlikely to be alone with Aston Villa also having been linked with him.
Sunderland have made just one signing to date since the end of the last campaign with former Villa defender Carlos Cuellar having headed for the Stadium of Light as a free agent.
But the departure of a series of players, including £9million keeper Craig Gordon, defender Michael Turner and Gyan, has given O'Neill scope to make significant additions.
He admitted last week that negotiations on several fronts were dragging on more than he would have liked, but remained confident of making a breakthrough.