Sources told ESPNNewYork.com and ESPN.com that the original offer to Lee was for six years and $140 million. Another source briefed on the talks told ESPN.com's Jerry Crasnick that the new offer is for less than the average ($23.3 million per year) of the original six-year offer.
SI.com first reported that the Yankees added a seventh year to their offer.
Meanwhile, the Texas Rangers stepped up their efforts for Lee, presenting a variety of increased offers to the free-agent pitcher in a face-to-face meeting in Little Rock, Ark., on Thursday.
"We reaffirmed our commitment to fielding a championship-caliber team and conveyed a menu of multiple offers which represented a substantial additional commitment for both years and dollars in an attempt to land his services," Rangers general managing partner and CEO Chuck Greenberg said Thursday night, though he wouldn't say whether the offers were for six years or more. He added that no timetable for making a decision was discussed during the meeting, which included assistant GM Thad Levine and co-chairman of the board Ray Davis, along with Lee, his wife, Kristen, and agent Darek Braunecker.
Yankees general manager Brian Cashman, reached at his office Friday afternoon, said nothing had changed since the Yankees presented Lee and Braunecker with their offer earlier in the week.
"The ball's in their court,'' Cashman said. "I have had no response to the offer we made other than, 'We'll get back to you.' We're in the same spot we were in yesterday.''
Rangers president Nolan Ryan was told of the Yankees' going to seven years on ESPN's "Mike & Mike in the Morning" earlier Thursday.
"We have to be concerned about that because seven years for any contract is really stretching it out," he said. "And I don't know how you predict how anyone is performing six or seven years from now."
Ryan didn't say that seven years exceeded the Rangers' limit, but he did say: "Everything has a ceiling that they have to understand what it is. And it doesn't make economic sense after a certain threshold."
Ryan was asked to gauge his team's chances in light of the development.
"Well, you know, if the reports that are coming out are true, obviously that makes it more challenging for us," he said.
Appearing on the "Ben and Skin Show" on ESPN Radio in Dallas, Rangers general manager Jon Daniels declined to say whether the Rangers would go to a seven-year offer.
"We've always planned on putting our best foot forward," he said.
Daniels wasn't shocked by the Yankees' reported offer.
"You look at the marketplace and you know what's been done before, so you know that could be a possibility," he said.
While admitting that the team is "willing to take on a level of risk that we wouldn't for another player," Daniels said the Rangers "also don't want to do something that's not in our best interests long-term."
Cashman said at the winter meetings in Florida on Wednesday that the team had made a formal offer to Lee, but Thursday wouldn't reveal details of the Yankees' plans.
"We will do what makes sense for us," Cashman said, adding that he had spoken to Yankees managing partner Hal Steinbrenner on Wednesday night.
Cashman said he was leaving the winter meetings and had no plans to make a detour to Arkansas to visit Lee and Braunecker. He said he is more than willing to meet with Lee again, if necessary.
To get some perspective on what Lee stands to earn, the $140 million, six-year offer falls between the contracts of the New York Mets' Johan Santana (6 years, $137.5 million) and the Yankees' CC Sabathia (7 years, $161 million).
The Yankees may eventually be willing to go to $25 million per season for Lee, according to a baseball official. With the Red Sox reportedly coming to terms with free-agent outfielder Carl Crawford, Lee's camp has even more leverage to get to $25 million per season and possibly seven years. The Yankees had been hesitant to offer Lee seven years.
"You scratch your head with some of the contracts we're giving out this week," Ryan said.
Lee remains the Yankees' No. 1 target. On Wednesday, Yankees manager Joe Girardi called him the "complete package."
"Cliff Lee has been the prize of this offseason and we will continue to pursue him," Girardi said.
Braunecker said Wednesday that one club is no longer involved in the Lee sweepstakes. He wouldn't say which team had been eliminated.
Ryan told ESPNDallas.com on Wednesday night that the Rangers had asked Braunecker to let them know what it will take to sign Lee. Ryan had expected it to take six years to sign Lee, and the club was considering doing that.
Braunecker said Thursday that he didn't appreciate that approach.
"We have no interest in participating in the unconventional negotiating style the club has requested," Braunecker told ESPN.com. "For the player to submit an offer to the club ... that's not the way the process works."
By Thursday afternoon, the Rangers had shifted gears and presented Braunecker and Lee with several different offers.
"You have to adapt to changing circumstances," Greenberg said. "When we heard late last night of the Carl Crawford signing, it didn't take too much analysis to figure out what the impact of that might be on our prospective competitors. As soon as we heard of that signing, we realized it was important we go to Little Rock and do it today, so we did so."
Greenberg said tactics change all the time based on circumstances.
"Early in the day we thought one avenue was the best and that changed," Greenberg said. "We adapted accordingly."
The Los Angeles Angels also have reached out to representatives for the free-agent left-hander, a source told Crasnick.
Greenberg said the Rangers' overall goal won't change whether Lee signs or not. And he made it clear that signing Lee would not handcuff the club from putting together a roster that can compete for championships.
"We certainly have a feel for where the market has gone," Greenberg said. "We've put a series of alternatives together for them that we think are highly competitive.
"The ball is in their court. We've given them a considerable amount to reflect upon. We want them to take it in. They need to digest it and decide where they go next."
Information from ESPNDallas.com's Richard Durrett, ESPN The Magazine's Buster Olney, ESPN.com's Jayson Stark and Jerry Crasnick and ESPNNewYork.com's Andrew Marchand was used in this report.