Numerous reports Tuesday, all citing unnamed sources, say the right-handed pitcher has agreed to a deal with the expectation of joining the Rangers rotation within a few weeks.
General manager Jon Daniels and assistant general manager Thad Levine didn't respond to messages. Team officials in the pressbox said they had nothing to report regarding Oswalt.
Oswalt was interested in joining the two-time defending American League champions during the offseason, but the Rangers were then set with their starting rotation.
But Neftali Feliz, the closer turned starter, went on the disabled list last week with right elbow inflammation and is not expected to pick up a baseball again until late June.