Source: Rangers eye Josh Beckett

BOSTON -- The Texas Rangers have not closed the door on a possible deal for Boston Red Sox pitcher Josh Beckett, according to a major league source, although the Red Sox have maintained they're not looking to move him and a rival general manager estimated there was a "2 percent chance" of a deal getting done.

"Too much money involved, and Beckett isn't pitching that well," the GM said.

Beckett, who is scheduled to pitch at Fenway Park on Tuesday night against the Tigers, declined to address his situation before the game.

"I've got nothing for you," he said.

Beckett is owed more than $36 million on the remainder of his contract -- $15.75 million in both 2013 and 2014 and more than $5 million for the final two months of the season. He is 5-9 with a 4.57 ERA in 17 starts. His strikeout ratio of 6.81 per nine innings is the lowest of the career, though his FIP (fielding independent percentage) is 3.52, ranking 28th among all pitchers with 100 or more innings this season. That's below his career FIP of 3.67.

General manager Ben Cherington has maintained publicly that the Red Sox are not actively trying to move Beckett, but multiple sources say the Sox have made it known Beckett is available, one major league executive going so far as to say that Boston was "trying to dump him."

The Atlanta Braves and Rangers are the clubs that have been mentioned as possible trading partners for Beckett. The Braves have little or no interest, one major league source said. The Rangers, however, are looking to add a pitcher, especially with Colby Lewis lost for the season and their chief rivals in the AL West, the Los Angeles Angels, adding Zack Greinke last week in a deal with the Milwaukee Brewers.

"He's been in discussion (for the Rangers) since last winter," one major league executive said Monday of Beckett. "Not a front-burner discussion, more of a 'What about this guy?' list. With that overall list getting smaller, it's like fish in a drying up pond -- things are getting more concentrated. The Rangers are in on all the fish, just waiting to see what breaks."

Despite reported interest by the Rangers in Phillies left-hander Cliff Lee, a source told ESPN.com's Jayson Stark on Monday that a Lee trade to the Rangers is "not going to happen." That would seem to keep alive a possible Beckett deal, although the Red Sox would have to absorb much of his remaining salary.

The Red Sox had shown interest in Miami Marlins pitcher Josh Johnson, and a Boston scout saw Johnson's last start in Miami, one in which he walked six. The same scout was in Atlanta to see the Marlins there; left-hander Mark Buehrle was pitching for the Marlins Monday night.

Buehrle signed a four-year, $58 million deal with the Marlins in the offseason, which would seem to rule out Miami looking to move him, but the Marlins already have traded pitcher Anibal Sanchez and infielder Hanley Ramirez, so it can't be ruled out. Buehrle is 9-9 with a 3.31 ERA and has walked just 23 batters in 130 2/3 innings.

The last major deal between the Marlins and Red Sox came in 2005, when the Sox sent Sanchez and Ramirez as part of a package that netted them Beckett and third baseman Mike Lowell in return.

The Red Sox also are trying to move Ryan Sweeney to the Cincinnati Reds, who are looking for a left-handed-hitting outfielder.

The Reds at least inquired about the availability of Jacoby Ellsbury, but the Red Sox have shown no indication of moving him now. He is eligible for free agency after the 2013 season, so this winter could be a different story.

The trading deadline is 4 p.m. Tuesday.

"I like my team," said Red Sox manager Bobby Valentine, who had an extended conversation with CEO Larry Lucchino in front of the dugout before Monday's game. "We're a good team. If there's any way Ben thinks we can improve it for this year and beyond, I'm sure he's going to do that.

"This is a good group of guys and I don't see any gaping holes. I see more holes on the other teams than I do ours."

Valentine also said, "I'm not getting traded. I've been assured of that."