Nimmo is currently out with a left index finger contusion.
Rojas said he won't play with Syracuse on Friday night, but could resume the rehab assignment on Saturday.
"That was one of the reasons why him and us wanted him to take at-bats before joining the team, just so he could test it," Rojas added. "He did the high velo machine but still wanted to do it live against pitchers."
As for Davis, Rojas gave a positive update.
"J.D. did high velo today, felt better. We're still aiming at tomorrow, but still gotta give us the feedback after hitting off the high velo machine," Rojas said. "So we can be in a good place to probably activate him tomorrow or the next day."
Both Nimmo and Davis suffered their injuries at Wrigley Field on May 1.
The Mets, who have won seven in a row, begin a three-game series against the Tampa Bay Rays on Friday night.