Ryan, who spoke with "Galloway and Company" on ESPN Dallas 103.3 FM on Monday afternoon, said general manager Jon Daniels, manager Ron Washington, pitching coach Mike Maddux and others will discuss the options in the coming days.
"If the group feels like they would like him to start this weekend against Colorado, I would be comfortable with that," Ryan said.
Oswalt pitched well in his latest minor league outing Sunday, allowing two runs and six hits with a walk and five strikeouts over six innings for Triple-A Round Rock in a 4-2 win against Oklahoma City. Five of the hits were singles with the only extra-base hit a sixth-inning double by Mike Hessman.
"The big thing was he got up to 100 pitches but he wasn't laboring to get there, which was encouraging," Rangers general manager Jon Daniels said before the Rangers faced the Padres in San Diego on Monday. "At this point, I think we feel like physically he's ready, he's as ready as he's going to be.
"You can always get better, but he's at a point if this was spring training we'd say he's ready to start the year. We've got to talk it over, look at the schedule, look at the club and the rotation and make a decision when he's going to come."
Ryan was in attendance at Sunday's start. Oswalt's next start could come on Friday and the question is whether it will be in the minors or with the Rangers.
"I thought he pitched to both sides of the plate last night and maintained his stuff throughout the game," Ryan said. "There wasn't a wow factor to his game, but the ball was coming out of his hand well. I thought he went about his business the way I would expect him to. He was making pitches and doing things I anticipated seeing him do."
Sunday was Oswalt's fourth minor league start and by far his best one. Through his first three starts in the minors (one for Double-A Frisco and two for Round Rock), Oswalt had a 7.71 ERA in 9 1/3 innings with eight strikeouts and three walks. In his start before Sunday, Oswalt threw 85 pitches and could get through just 3 1/3 innings in Frisco, allowing three runs on five hits.
The Rangers signed Oswalt after Neftali Feliz went on the disabled list with a sprained elbow ligament. He's out until at least July 18. But shortly after that, Derek Holland was forced to the DL with a stomach ailment and a sore shoulder and most recently Alexi Ogando was placed on the 15-day disabled list with a strained groin. Holland and Feliz are throwing again off flat ground with Holland expected to be the first of the trio to return.
The injuries have tested the club's pitching depth with Double-A pitcher Justin Grimm getting called up on Saturday to start against the Houston Astros. He worked six strong innings in winning his major league debut.