When asked if he thought his closer had a chance to reach that mark, however, manager Mike Scioscia said he thinks it all depends on the team's offensive production.
Scioscia pointed out that the Angels have struggled to get runs across the plate this season. They've been held to five runs or fewer in 25 of their past 31 games -- compiling a 16-9 record in those games -- and Los Angeles is currently 11th in the American League in runs scored.
"If our starting pitchers continue to pitch as deep and as well as they have and we're not scoring runs, he might end up with 100 saves," Scioscia said.
Rodriguez is one of the primary reasons the Angels are 46-30 despite their low run totals. In addition to Los Angeles' 16-9 record in games in which it scores five runs or fewer, the Angels are also 31-13 in games decided by two runs or fewer and they have 14 wins when scoring three or fewer. The last number is tops in the Major Leagues.
Scioscia said he doesn't expect his club to continue hitting like they have so far this season, and recent results would suggest he's right. The Angels have scored six runs or more in four of their past six games.
Additionally, four Angels regulars have hit above their season average in the past 30 days. Leading the way is Vladimir Guerrero, who leads all Major Leaguers with a .433 batting average in June.
All of the above are reasons Scioscia has confidence that his offense will improve and eventually flourish, which could affect Rodriguez's chance at breaking Thigpen's record.
"If our offense can get into the game like I know is in this group of guys -- and we continue to pitch -- there may not be as many save opportunities as there have been to this point, so the numbers might not get there," the manager said.
Still, Scioscia recognizes Rodriguez's contribution to Los Angeles' immense success to this point, and he praised the prolific closer for being a consistent force for his team every time he's called on to save a game.
"He's answered the bell for all of them," Scioscia said.
Zachary Osterman is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.