The veteran bench player, who had his roughest season in the majors in 2014, has initial interest from three teams.
Scott Hairston and Ross Detwiler didn't make the roster, while Rafael Soriano and Jerry Blevins did.
Hairston has three at-bats this month, his last on June 6. Zimmerman could spell Adam LaRoche at first.
The veteran backup outfielder is back after missing 26 games with a strained left oblique.
Minor updates on the health of all three players. Gonzalez felt minor shoulder tightness in his Wednesday start.
Zimmerman is exercising with an immobilized right thumb and Hairston took his first on-field batting practice since injury.
Scott Hairston landed on the disabled list with an oblique strain and Tyler Moore replaced him on the Nationals' roster.
Matt Williams didn't guarantee veteran Scott Hairston a spot on the roster, but he also didn't say he doesn't have a spot.
Manager Matt Williams is playing the backups often early, but will use the regulars more as the season approaches.
Scott Hairston may give Davey Johnson the right-handed first base option he has been lacking.