The Seagulls have followed gaining promotion to the Premier League by remaining clear of the relegation zone, with seven points currently separating the club and 18th-placed Southampton.
The 59-year-old is quoted by The Argus as saying: "We have a chairman who has resisted any of our players moving on in recent windows and hopefully that will happen again.
"Any interest in any of our players is recognition of the season they've had and hopefully a season the club has had. That's part and parcel of your work at a football club, but keeping our best players is top of our requirements."
Dunk has started each of the club's 34 top-flight fixtures this season, while Gross has contributed six goals and eight assists in his first campaign at Brighton.