Manchester United manager Louis van Gaal has refused to rule out the possibility of signing goalkeeper Victor Valdes.
Manchester City boss Manuel Pellegrini says he is confident that England goalkeeper Joe Hart will sign a new contract.
Press Association Sport understands the Black Cats have made a formal offer for the 25-year-old Scotland international after months of speculation over his future.
Fletcher, who has two years remaining on his contract at Molineux, is understood to be among manager Martin O'Neill's main targets this summer as he attempts to plug the gaps left by Asamoah Gyan and Nicklas Bendtner.
However, relegated Wolves reportedly value the player at around £10million, and it remains to be seen whether or not Sunderland's bid comes close to persuading them to sell.
Former Hibernian frontman Fletcher joined the Black Country club from Burnley two summers ago, and although he personally has performed creditably in the Barclays Premier League, has been relegated twice during his time in the English top flight.
O'Neill has, to date, made only one signing since the end of last season after completing a move for free agent Carlos Cuellar following the expiry of his deal at Aston Villa.
At the same time, a procession of players have headed out of the Stadium of Light, many of them from the fringes of the senior squad, but including the likes of Gyan, Scotland keeper Craig Gordon and central defender Michael Turner.
The Ulsterman revealed last week that the club was monitoring several situations and that he hoped to make a breakthrough soon.