Young was suspended for one week by Major League Baseball last month for his arrest on aggravated harassment charges in New York, stemming from an anti-Semitic rant against a panhandler.
Tigers manager Jim Leyland said he doesn't plan to start Young on Friday but he will be available to play.
Young, who was placed in a treatment program by MLB, was hitting .242 with one home run and five RBIs in 18 games before his arrest.
Eldred, 31, was called up from Triple-A Toledo last Friday after hitting .388 in 20 games. However, he hit .188 in five major league games.
If Eldred is not claimed on waivers, then he could be sent back or Toledo or he could request his release from the organization.