Fielder, 27, has played his entire seven-year career in Milwaukee, but made waves last year by publicly announcing that it would most likely be his last year with the club.
Last season, the burly infielder played in all 162 games while hitting .299 with 38 home runs and 120 RBI for the NL Central champs.
Should Fielder decline arbitration and sign with another team, the Brewers would be in line to receive draft compensation.
Rodriguez, 29, was dealt to the Brewers prior to the trade deadline last season by the New York Mets. He appeared in 42 games last season for New York, recording 23 saves.
Once he arrived in Milwaukee, he became a setup man for closer John Axford, going 4-0 with a 1.86 earned run average in 31 appearances.
Rodriguez also set a new major league record for saves in a season by recording 62 for the Halos back in 2008.
Milwaukee would again receive draft picks if Rodriguez declines arbitration and signs with another team.
The Brewers also declined arbitration on Type-B free agent shortstop Yuniesky Betancourt.
Betancourt hit .252 with 13 home runs and 68 RBI last season, his first with Milwaukee.