The Bears picked up Santos last month to replace Connor Barth, but Santos tweaked a groin muscle prior to Chicago's 15-14 loss to San Francisco.
Santos was also released by the Kansas City Chiefs earlier in the year because of an injury.
Nugent kicked in four games for the Dallas Cowboys this season. He made 7 of 9 field goals in those games, filling in for the injured Dan Bailey. Prior to his stint in Dallas, Nugent spent seven seasons with the Cincinnati Bengals, from 2010-16.
Nugent was 23-of-29 last season in Cincinnati but was released on Dec. 13, 2016, after missing five PAT attempts in five games.
The Bears face the Bengals on Sunday.