Phillips, a two-time All-Star, batted a career-best .300 with 18 home runs and 82 RBI for the Reds this past season, his sixth with the team.
The Reds also declined their team option on closer Francisco Cordero for next season.
Cordero was 5-3 with a 2.45 earned run average with 42 strikeouts, 22 walks and 37 saves.
Thompson appeared in one game last season and was shelled, giving up five runs on six hits in a 10-4 loss to the Philadelphia Phillies.
Burton appeared in six games for the Reds, posting no record with three walks, three strikeouts and a 3.86 ERA.
In 18 2/3 innings last season, Maloney was 0-3 with a 9.16 ERA, 13 strikeouts and four walks.