The Atlanta Braves are still involved in discussions with the Mets, but the Rangers and Giants are moving along in talks with New York.
When Beltran signed his seven-year, $119 million contract with the Mets in January 2005, it included a complete no-trade clause that requires him to give permission before the Mets deal him.
Sources said Wednesday that the Cleveland Indians offered to take on Beltran's entire salary for the rest of the year, but were told that the outfielder would not consider going to Cleveland. The Indians walked away from the talks convinced that Beltran's agent, Scott Boras, is in control of the process.
At least for now, the Boston Red Sox also are out of the Beltran sweepstakes, a league source told ESPNBoston.com's Joe McDonald.
The source said that the Giants are the front-runners after the Rangers got close to making a deal, but it fell through.
Red Sox general manager Theo Epstein had been talking with Mets GM Sandy Alderson, and the Mets have been heavily scouting Boston's minor league system.
Major League Baseball's trade deadline is 4 p.m. ET Sunday.
Amid speculation that Beltran might be hesitant to leave the National League for an American League team, Boras told ESPN.com's Jerry Crasnick on Tuesday that one factor trumps all.
"This decision for Carlos is about the select group of teams where he feels he has a great chance to win," Boras said. "That's what this thing is about."
Beltran also has said he is not interested in serving as a designated hitter.
Buster Olney is a senior writer for ESPN The Magazine.