Moore (Tommy John surgery) pitched for Triple-A Durham on Saturday night -- making his fifth rehab start -- and allowed two earned runs on five hits and three walks while striking out eight in five innings. The left-hander threw 94 pitches, 56 for strikes.
"He'll get back here at some point [Sunday] and we'll most likely insert him into the rotation five days from [Saturday]," Rays manager Kevin Cash said.
Cash did not give reporters an exact date, but he did allow that Moore won't be inserted into the rotation any earlier than five days. However, he could be added later.
Meanwhile, Odorizzi (left-oblique strain) felt fine Sunday morning after throwing 51 pitches during a three-inning batting practice stint Saturday. He will pitch for Class A Charlotte on Thursday in Bradenton, Fla.
Cash couldn't say when the right-hander will be back in the rotation, but it should be soon.
"We haven't got there yet," Cash said. "We have to sit down and talk about a lot of different things. With the break and how we're going to factor in the starting pitching, we haven't quite got there."
• Andrew Bellatti (right shoulder tendinitis) felt fine after throwing 26 pitches during a batting practice session Saturday. He said he will head for a rehab assignment at Charlotte on either Tuesday or Wednesday. The Rays would like to get the right-hander built back up to where he can throw 50-plus pitches.
• John Jaso (left wrist contusion) served as Charlotte's DH Saturday night and went 2-for-3 with a walk. And James Loney (left middle finger fracture) hit on the field Sunday and ran the bases. Both are close to returning.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.