The Rangers are scheduled to meet with free agent right-handed starter Roy Oswalt on Monday, a source confirmed Sunday afternoon.

The meeting was first reported by The Dallas Morning News.

ESPNBoston.com reported this weekend that Oswalt was close to a deal with the St. Louis Cardinals and various reports have suggested the pitcher’s preference is either St. Louis or Texas.

Other teams have also pursued Oswalt, including the Boston Red Sox. CBSSports.com reported Friday night that Oswalt had rejected a one-year offer from the Detroit Tigers.

Oswalt, 34, is currently looking for a home in 2012 after a bothersome lower back landed him on the disabled list twice in 2011. The veteran was 9-10 with a 3.69 ERA in 139 innings (23 starts) with the Philadelphia Phillies, who declined to pick up his option after the season. After Oswalt was dealt to the Phillies at the trade deadline in 2010, he went 7-1 with a 1.74 ERA the rest of the season (12 starts). He was a consistent starter in Houston, winning 20 games in 2004 and 2005 and has a career 3.21 ERA.

The big question for Texas is whether he's a fit here. The Rangers head to spring training with more than a full rotation with the signing of Yu Darvish. Joining the 25-year-old Japanese star as a starter in Surprise, Ariz., next month is Colby Lewis, Derek Holland, Matt Harrison, Alexi Ogando and Neftali Feliz. Ogando is the leading candidate to move to the bullpen.

Oswalt has said through his agent during this offseason that he'd prefer to start. So if he signs with Texas, that would require another move -- either putting someone in the bullpen or making a trade. Matt Harrison could be one pitcher involved in those dominoes. He said Saturday that he isn't worried about it.

"My goal is to come in there and be the best I can be and make sure no matter what, I give it everything I have in spring training and it will be left in their hands if they want me in the rotation," Harrison said before signing autographs at the Rangers' Winter Caravan in Frisco. "I feel like I was able to prove I can be a consistent starter last year and hopefully they believe in that and they saw that and they want me to stay in the rotation. It’s out of my hands whether or not they want to put me in the bullpen if they sign Roy or whatever happens from there."

Rangers general manager Jon Daniels said on ESPN Dallas 103.3 FM on Friday that he was “intrigued” by the depth that Oswalt could provide to the staff, but wasn’t sure it was a perfect fit, either.

"If that were to happen, you’d love to have extra depth," Daniels said on 'The Ben and Skin Show' on Friday morning. "The flip side we’ve got to consider is what if that doesn’t happen? How does it all fit together? We've spent a lot of time and resources developing this younger group where they are ready to maybe take that next step and do we owe it to them? Those are things we’re walking through right now."