LAKE BUENA VISTA, Fla. (WFAN/AP) — How hungry are the New York Yankees to sign Cliff Lee?

Ken Rosenthal of is reporting the Texas Rangers, who met with Lee on Thursday plan to increase their off to Lee above their current offer of five years.

According to WFAN’s Jon Heyman, the Yankees have added a seventh year to their initial six-year, $137-140 million offer for the prized free agent.

“Yankees have just gone to a seventh year for Cliff Lee. Werth and Crawford getting seven, it’s only right,” reports Heyman.

According to Rosenthal, Boston was one of two “mystery” teams offering Lee a seven-year contract, but that offer was “for a lower dollar figure than Lee would accept.” With added leverage, Lee’s agents would then force the Yankees to up their bid from six years to seven.

Yankees general manager Brian Cashman spoke Wednesday night regarding the Lee offer.

“Hannibal Lecter in a straitjacket right now, waiting on this Cliff Lee thing,” the Yankees general manager said.

Every other possible big move by New York must wait until the 32-year-old left-hander decides. “It’s kind of restricting my movements a little bit,” said Cashman.

LISTEN: Yankees GM Brian Cashman on Lee offer

Lee’s agent, Darek Braunecker, left the winter meetings and headed to Arkansas to meet with his client after receiving the offer from the Yankees. New York manager Joe Girardi even called Lee “the prize of this winter.”

Cashman wouldn’t discuss his dinner meeting with Carl Crawford on Tuesday night — other than to say he had steak — and wouldn’t say whether the Yankees could sign both Lee and the All-Star outfielder. That possibility became moot Wednesday night when Crawford reached a preliminary agreement on a $142 million, seven-year contract with the Boston Red Sox.

Admitting he was tired, Cashman playfully discussed his job as GM of baseball’s highest-revenue franchise and thanked his bosses for giving permission to make the offer to Lee.

“I know my title is general manager, but I consider myself the director of spending of the New York Yankees. I don’t make it. I spend it,” Cashman said. “We’ve made an offer that’s not easy to be making and I appreciate the fact that the Steinbrenners are allowing us to make an offer to this degree. … It’s a big commitment on behalf of the fan base, and we’ll see what happens. I think we’ve done all we can do from meeting to talking to showing.”

New York almost acquired Lee from Seattle in July before he was dealt to Texas. Lee then helped the Rangers beat the Yankees in the AL championship series, putting Texas in the World Series for the first time.

“He’s a guy that wins. He’s a guy that gives you innings. He’s a guy that knows how to pitch on the big stage,” Girardi said. “Everything that you’d want, and a guy that you would ask to help you win another championship. This is a guy that has great command, never beats himself, he holds runners, has a mixture of four pitches that he can use at my time. He’s the complete package.”

Cashman met Lee in Arkansas on Nov. 10 but waited to make an offer until the pitcher was closer to decision-making mode.

Texas hopes to re-sign Lee, pointing out how close the team is to the pitcher’s home in Arkansas. Lee is close to New York ace CC Sabathia, his former Cleveland teammate, and the Yankees hope that helps them in a thus-far deliberate process.

“He’s got all the information he needs from us. I assume he’s got the same from anybody else who’s got an oar in the water here,” Cashman said. “They’ve gone through Cleveland and they’ve gone through Philly and they’ve gone through Seattle and they’ve gone through Texas for the right to free agency. They’re here. So they want to make the right decision.”

NOTES: LHP Andy Pettitte called Cashman on Tuesday and said he hoped New York signs Lee. Cashman sounded more hopeful Pettitte will return for 2011. “If I had to bet at some point, I think he’ll play, but he’s telling me right now he’s leaning the other way.” … Girardi has talked with Jorge Posada about the plan to switch him from primarily a catcher to mostly a DH. “He understands. But I still think that he wants to catch. I mean, that is his first love, that is his first passion. To me this gives him a chance to extend his career, stay healthy, and be productive for us.” … OF Brett Gardner had inflamed tissue removed from his right wrist by Dr. Melvin Rosenwasser. Gardner is expected to be ready for spring training.

Copyright 2010 The Associated Press.

Watch & Listen LIVE