Moore allowed three runs in three innings in a loss to the Astros on Sunday, leaving him 1-5 with a 7.82 ERA in nine games (eight starts). His only win came against the Rays on April 17. He is 0-2 with a 12.79 ERA over his last three starts.
"We've got to continue to show some progress," Banister said. "It's an ongoing evaluation of where we are at. He has shown flashes of throwing the ball well. At this point, we don't have any plans to make a move in the rotation."
The Rangers are missing Martin Perez, who is on the disabled list with soreness in his right non-throwing elbow and is not expected to return soon. If the Rangers need another starter, Banister said their options are left-hander Yohander Mendez and right-hander Austin Bibens-Dirkx, who are both at Triple-A Round Rock.
Reliever Jesse Chavez does not appear to be a favorable option, even though he has pitched well as a long/middle reliever.
"Right now, Chavez is doing a great job in the bullpen," Banister said. "It doesn't mean he's not an option, it just means we like what he is doing for us right now."
Rangers beat • Right-hander Chris Martin (right forearm irritation) pitched a scoreless inning for Double-A Frisco on a rehab assignment on Monday. Martin is scheduled to throw another inning on Wednesday.
• Reliever Brandon Mann, who made his Major League debut on Sunday, turns 34 on Wednesday. He is the second oldest player to make his Major League debut for the Rangers, behind only Yoshinori Tateyama, who was 35 in 2011.
• Right-hander Tim Lincecum allowed a run in 1 1/3 innings for Round Rock on Monday, earning the win. He has pitched 4 1/3 innings over four appearances, allowing six runs (four earned) on seven hits and four walks while striking out five.