The Yankees met for several hours on Tuesday with Jeter's agent, Casey Close, sitting down in Tampa, Fla., for a session that reiterated the wishes of both sides to reach an agreement and keep Jeter in the only uniform he has ever worn.
Positive talks between the Yankees and Jeter's camp continued on Friday, according to a tweet from Newsday's Ken Davidoff.
The Associated Press reported Thursday that the club increased its contract offer to Jeter. The team informed Jeter's side of the new offer during a telephone conversation early Thursday, a person familiar with the negotiations told the AP.
"The ball's in Derek's court now, and his agent," Yankees co-chairman Hank Steinbrenner said later Thursday in a telephone interview with The Associated Press. "It's up to them."
Close declined comment.
"We don't know how happy they are. We'll see," Steinbrenner told the AP. "There's no possible way anybody could criticize us for what we've offered."
New York had opened the negotiations last month with a $45 million, three-year offer last month.
Jeter's camp has been said to be seeking four or five years worth approximately $23 million per season, but the Yankees do not appear inclined to go that high for the shortstop, who turns 37 in June and is coming off a year when he posted a career-low .270 batting average.
While Close earlier referred to that position as "baffling" and compared his client to a modern-day Babe Ruth, the Yankees are emboldened by the fact that no other team is likely to top their existing offer for Jeter.
Most in baseball believe that Jeter will eventually wind up back in New York, and no other club has gone so far to extend an offer.
Elsewhere in baseball, the agreement struck between the Rockies and shortstop Troy Tulowitzki would figure to bolster the Yankees' case.
Tulowitzki inked a contract extension that will pay him an average of $15.7 million over the next 10 years, making the 26-year-old, who grew up idolizing Jeter, the highest-paid middle infielder in the game.
The Yankees could top Tulowitzki's deal, paying Jeter more than that $15.7 million per year, while still reducing the $18.9 million average annual salary issued in Jeter's last deal.
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.