Derek Jeter, left, celebrates with Mark Teixeira. According to sources,...

Derek Jeter, left, celebrates with Mark Teixeira. According to sources, Jeter and the Yankees are moving closer to a deal. (Sept. 27, 2010) Credit: AP

Hank Steinbrenner has been mostly quiet for the better part of two years. But the eldest son of George Steinbrenner, pushed into the background by his younger brother Hal, is roaring again, inserting himself into the Derek Jeter negotiations.

The Yankees increased their original three-year, $45-million offer to Jeter yesterday, according to an industry source, and Jeter's agent, Casey Close, lessened his demands on behalf of his client. They had been seeking a four- or five-year contract worth $23 million per season.

"The ball's in Derek's court now, and his agent," Hank Steinbrenner told The Associated Press last night. "It's up to them."

He said later: "We don't know how happy they are. We'll see. There's no possible way anybody could criticize us for what we've offered."

The figures discussed were not immediately known, and a source, while acknowledging the positive nature of the talks, said a deal "isn't close" yet.

Hank Steinbrenner no longer is in control of the Yankees, though his overseeing of Alex Rodriguez's 10-year, $275-million contract in 2007 - a deal struck after A-Rod opted out of his 10-year, $252-million deal during the final game of the World Series - hovers over these talks.

The negotiations with Jeter, dormant as the week began, have accelerated, though it still is not clear if a deal can be struck before the winter meetings, as the Yankees desire. The meetings begin Monday in Orlando, Fla.

Jeter, who made $21 million last season, doesn't want to take a pay cut, something that almost assuredly will have to occur for a deal to get done. The length of the contract he is asking for also is an issue for the Yankees.

This week has been much more positive than last week, when Close called the Yankees' negotiating strategy "baffling" and Brian Cashman fired back that Jeter was free to explore the free-agent market if he didn't like the team's offer.

The thaw started Tuesday when Close flew to Tampa to meet with Jeter. The two then met for nearly five hours with managing general partner Hal Steinbrenner, team president Randy Levine and Cashman.

No offers were exchanged during that meeting and the Yankees hoped a counter-offer from Jeter would come Wednesday. No conversations took place Wednesday, but a source said there were "a bunch" of conversations yesterday as both sides, who agree they need each other, moved from the original numbers proposed.

Hank Steinbrenner was not at Tuesday's meeting but spoke with his brother shortly after it ended and said he was "confident" a deal would be struck.

Cashman and Close did not return calls yesterday.

Notes & quotes: Rangers president Nolan Ryan came away from Tuesday's meeting with Cliff Lee optimistic. "I think if we're competitive, we're going to get a lot of consideration," Ryan told ESPNDallas yesterday. The Rangers did not make an offer, nor has any other team. "It's no secret we want Cliff, and we will do what we can to get him," Hank Steinbrenner told AP. "That's the bottom line." . . . The Yankees signed Sergio Mitre to a one-year, $900,000 deal. They did not offer contracts to Alfredo Aceves and Dustin Moseley, allowing both to become free agents.

NewsdayTV's Doug Geed visits two wineries and a fish market, and then it's time for holiday cheer, with a visit to a bakery and poinsettia greenhouses. Credit: Randee Dadonna

Out East with Doug Geed: Wine harvests, a fish market, baked treats and poinsettias NewsdayTV's Doug Geed visits two wineries and a fish market, and then it's time for holiday cheer, with a visit to a bakery and poinsettia greenhouses.

NewsdayTV's Doug Geed visits two wineries and a fish market, and then it's time for holiday cheer, with a visit to a bakery and poinsettia greenhouses. Credit: Randee Dadonna

Out East with Doug Geed: Wine harvests, a fish market, baked treats and poinsettias NewsdayTV's Doug Geed visits two wineries and a fish market, and then it's time for holiday cheer, with a visit to a bakery and poinsettia greenhouses.

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