Poche (back) threw on flat ground Sunday and is expected to throw a bullpen session Monday, MLB.com reports.
Poche (back) is not expected to spend much more than a minimum stint on the injured list, MLB.com reports.
The Rays placed Poche on the 15-day injured list Friday, retroactive to April 24, with mid-back tightness, Ryan Bass of Bally Sports Sun reports.
Poche earned the save in Thursday's 2-1 win over Anaheim, working around a pair of hits while striking out one in the ninth inning.
Poche signed a one-year, $2.375 million contract with the Rays on Thursday to avoid arbitration, Mark Feinsand of MLB.com reports.
Poche (4-1) earned the win in Wednesday's 4-3 win over the Cubs, allowing one hit over a scoreless inning.
Poche lost his arbitration case against the Rays on Saturday, meaning he'll make $1.175 million this season, Mark Feinsand of MLB.com reports.