Back-to-back 2-1 wins, against Brighton in the Sky Bet Championship and Chesterfield in the Capital One Cup - the latter aided by Brown's superb 25-yard strike - have made it a dream start to the season for Brian McDermott's side.
Leicester have made an identical start, against Middlesbrough and Wycombe, and will pose a tough test for Leeds.
Brown told the Yorkshire Post: "Winning is a great habit, though we know we have some tough games coming up - starting with Leicester on Sunday.
"It will be tough as they are expecting to do well. But I am sure we will have a great following and we will give it everything."
Brown's goal on Tuesday made up for missing out on the team against Brighton, and competition for a midfield place has increased further with Rudy Austin's return from suspension.
"On a personal level, I want to get some minutes, for sure," Brown said. "It will be a long season if I am not involved at all. I'm here as long as the manager wants to keep me involved.
"Not only on the pitch but off it as well. I train hard, still feel fit and hope to do my bit."
Both teams will be at full strength, with El-Hadji Diouf back in contention after injury for Leeds.
Leicester's Zak Whitbread and Ben Marshall return after missing the midweek Capital One Cup win over Wycombe.