Springer will play in an alt site game against the Miami Marlins on Saturday evening after returning to action on Friday night in an intrasquad game.
"He feels better from what he did yesterday. ... He's doing fine today," Montoyo told reporters when asked how Springer was doing physically following Friday's intrasquad game.
Montoyo said if all goes well following Saturday's action, "the hope" is Springer will be able to return to the Blue Jays lineup next week.
Springer is rehabbing from a low-grade quad strain suffered in the first week of April, an injury that immediately followed an oblique strain that landed the 31-year-old on the injured list to start the 2021 campaign.
Pitcher Nate Pearson will also take part in Saturday's alt site game as the 24-year-old works his way back from a groin injury. Pearson is expected to pitch two to three innings on Saturday.
The Blue Jays continue their series in Tampa against the Rays on Saturday, with first pitch slated for 6:10 p.m. ET/3:10 p.m. PT.