Maiava, a fourth-round draft pick who while at Southern California was twice named the Trojans' co-special teams player of the year, had six tackles, including two on kickoff coverage, during the Browns' 27-10 victory over the Detroit Lions in a preseason game Saturday.
''He's gotten better in the last couple weeks in terms of his production on special teams,'' Mangini said Tuesday. ''That was something he was very good at USC, and he also, when he got a chance, was a pretty good defensive player. It took a little time, he had to work into a role and what I'm looking for is kind of the same thing from him as everybody else.
''What are you going to do on teams? And then that gets you to the 53 (-player roster). Are you good enough to get to the 45? If you're on the 45, you're always live, because at any point you could be in the game. So, that's what I'm looking for from him, is to keep carving that out.''
NFL rosters must be cut down to no more than 75 players by Tuesday, and must be at 53 by Sept. 5.
Maiava has eight tackles in two preseason games -- he ranks second on the team, two behind Kamerion Wimbley. All eight of Maiava's tackles are solo stops, best on the Browns and tied for 18th among all NFL linebackers in the preseason.
Cleveland will play at home against the Tennessee Titans on Saturday before finishing its exhibition schedule on the road against the Chicago Bears on Sept. 3.
The Browns will open their regular season at home against the Minnesota Vikings on Sept. 13.