The 23-year-old, who joined Rovers from non-league Hayes and Yeading in 2011, will be out of contract at the end of the season.
"I'm really enjoying my football at Bristol Rovers," Brown told Sky Sports News.
"The fans and manager have been behind me. I want to focus doing well with this team. It's a strong league, but we've got more than enough quality in the squad."
It is believed that Rovers could be forced to accept a fee in January rather than lose the defender for nothing at the end of the season.