"We have actually had a few bids for quite a lot of our players because we have got some good players here and maybe people think we could be easy pickings. But we are not," Moyes said, confirming a bid for Van Aanholt had been turned down.
Sunderland, currently 18th in the Premier League, also rejected a 6 million pound bid for striker Jermain Defoe from West Ham United last week.
"I want to keep all my good players, I want to keep them here. I want to try to build, I want us to add to our group rather than lose players," Moyes said.
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Sunderland, who host 11th-placed Stoke City on Saturday, have lost just twice on home soil since September and the Scot is hoping for the run to continue against the Potters.
"We've played a lot better at home and we look as if we're capable of getting results," Moyes said.
"We didn't get them at the start of the season but we've settled down and we're beginning to give the supporters something to shout about."
(Reporting by Hardik Vyas in Bengaluru; Editing by Ian Chadband)
