Dunk, who missed the end of last season before being cleared of sexual assault, spent time on loan at Bristol City earlier this season but is now back in the first-team squad after being a regular under former manager Gus Poyet.
"I remember Gus picking him out from a young age and rated him and played him. Gus had a lot of faith in him, we have as well," Jones told the Argus.
"Lewis has had certain issues in terms of a year which he probably missed mentally. Now we've asked him, we've spoke to him, we are looking at him for a long-term future here."
Dunk made his debut for Brighton in May 2010.