The 59-year-old, who has enjoyed spells managing in Israel and Kazakhstan in recent years, has helped the Reds to a string of impressive results since taking charge in December.
Despite being linked with clubs in the Championship, Gregory insists that he is instead looking ahead to the future with his current side.
"I'm more ambitious for the club than I am for myself," the former Aston Villa manager is quoted as saying by Crawley News. "If the club are successful then I'm happy. I'm coming up to 60 on my next birthday, and the simple fact is I've been elsewhere and I've done a lot of things.
"Now my focus is more about improving the club than improving myself. Crawley is a great opportunity and I want to try to get things as good as they can be. I would love to see Crawley in the Championship.
"Next season I would seriously love to be challenging all season; in the top six from start to finish. I see no reason why we shouldn't if we recruit the right people in the summer."
Crawley are currently 14th in the League One table.