Texas still leads Roy Oswalt hunt

Updated: May 29, 2012, 6:06 PM ET

The Los Angeles Dodgers watched pitcher Roy Oswalt throw last week in Starkville, Miss., a baseball source said. But team officials are convinced that Oswalt is going to sign with the Texas Rangers -- possibly as early as this week.

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Oswalt, who had previously auditioned for the Philadelphia Phillies, Boston Red Sox and the Rangers, has given teams indications that Texas is his destination of choice. He has a close relationship with club president Nolan Ryan, and he apparently likes the thought of pitching for a contending team that's close to his Mississippi home.

"I would be shocked if he doesn't go to Texas," a baseball official said. "A team is going to have to greatly outbid Texas to keep him from going there."

Oswalt, 34, has a career record of 159-93 in 11 seasons with Houston and Philadelphia. He is a three-time All-Star who has finished among the top five in National League Cy Young Award balloting five times in his career.

After waiting until spring training and failing to land a job to his satisfaction, Oswalt told major league clubs in late February that he planned to wait until midseason to return.

Several contending clubs recently have incurred injuries that could heighten the interest in Oswalt.

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Texas lost pitcher Neftali Feliz to the disabled list with a shoulder injury, and the Rangers have filled his spot in the rotation with Scott Feldman. But general manager Jon Daniels recently told reporters that "everything is on the table" when it comes to strengthening the pitching staff, and manager Ron Washington said he would be on board with bringing in Oswalt.

The Phillies are waiting for an update on Roy Halladay, who was to visit a doctor Tuesday to have his sore right shoulder examined.

The Dodgers have a void in their rotation now that Ted Lilly has gone on the disabled list with a shoulder injury. But they expect Lilly to return by late June, and the current plan calls for Nate Eovaldi to assume his spot in the rotation.

Eovaldi, 2-2 with a 3.09 ERA in nine appearances with Double-A Chattanooga this season, is scheduled to start Tuesday night against Milwaukee.