Brown said the team will sit down with Manziel before making a decision.
"I know a lot's been written about him," Brown said during a press conference. "What we expect is Johnny to have a good offseason and be ready to go. We're not in any panic to make any decision one way or another on him.
"He understands what's ahead of him and what he needs to do to have a career in this league and with the Browns."
Manziel has been a constant distraction for the team during his two seasons in Cleveland. The latest one involved his whereabouts the final weekend of the regular season.
There are published reports saying Manziel was in Las Vegas when he wasn't with the club for the regular-season finale. Brown said the organization remains in the dark about where Manziel was even though it fined Manziel for missing a scheduled medical treatment on Jan. 3.
"We don't know where Johnny was," Brown said. "I don't know where Johnny was the final game of the season."
The decision regarding Manziel's future will also come down to what new coach Hue Jackson thinks. A recent published report claims Jackson would prefer to part ways with Manziel.
Cleveland has the No. 2 overall pick in the upcoming NFL Draft. Jackson might want to find his quarterback of the future in the draft.
Brown said the club will also sit down with wide receiver Josh Gordon if he is reinstated by the NFL. Gordon missed all of last season due to a suspension for violating the league's substance abuse policy a third time.
Gordon applied for reinstatement on Wednesday.