HITC Sport understands that Black Cats want to keep other assets.
West Ham United are trying to land Defoe and have had more than one bid rejected, but they are ready to return with a new offer.
And HITC Sport also understands that Crystal Palace, now under the charge of their former boss Sam Allardyce, have made contact over both Kone and van Aanholt.
Sunderland's Jermain Defoe
Sunderland are loathed to lose any of their key assets, of which Defoe, Kone and van Aanholt rank amongst, but with owner Ellis Short insisting sales are needed before investment - they may find a big offer hard to turn down.
That is one reason that Sunderland's hierarchy are looking at other deals, and one of the most valuable assets amongst the rest of the squad is Borini.
The Italian international has recently returned to full fitness, and boss David Moyes was quick to use him but he also that he may have to let him leave to guarantee the futures of others.
The likes of AC Milan and Roma have been linked with the 25-year-old, whilst HITC Sport understands there is interest from both Major League Soccer in America and also from the Chinese Super League.
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