In addition, there was other good news on Saturday about Andrew Bellatti, Jake Odorizzi, Tim Beckham and John Jaso.
Moore, who is in the home stretch of his rehab from Tommy John surgery, is expected to throw 90 pitches.
Rays manager Kevin Cash did not have an answer when asked if Moore will have one or two starts after Sunday's.
"It will be up in the air," Cash said. "We'll have to sit down and talk. I don't think anybody's completely clear on what to do after that. We'll kind of evaluate after his start."
Cash said one of the benefits of having Moore pitch in a Triple-A game rather than Class A is having to face tougher at-bats.
"Some more veteran hitters," Cash said. "I don't think there's much you can do to emulate pitching in a Major League environment. It's fair to think that's as close as you can.
"You want to have some guys have quality at-bats, make him make some quality pitches. Maybe throw some different pitches that you wouldn't throw in a Single-A game. Not disregarding Single-A. It's nice we have an affiliate close to us so we can use that."
• Bellatti (right shoulder tendinitis) and Odorizzi (left oblique strain) both threw "light bullpens" on Saturday when they pitched from the mound, but the catcher was positioned in front of home plate.
"They both reported feeling really, really good," Cash said. "So that's good to hear about both of them."
Monday, both right-handers will throw full bullpens.
• Beckham (strained right hamstring) played in an extended spring training rehab game on Saturday.
"Got some at-bats, felt fine, ran some balls out, so that's a good sign," Cash said.
• Jaso, who has been out since the first game of the season with a left-wrist contusion, took live batting practice for a second consecutive day on Saturday.