Torii Hunter has received two five-year offers on the free-agent market from other teams, but the Twins have not budged from their three-year, $45 million offer, a person close to the negotiations said Tuesday.
Hunter's agent, Larry Reynolds, called Twins General Manager Bill Smith in an attempt to spur their talks last week, and neither side has come forward with a new proposal.
Asked if he was confident the Twins would get a final shot to negotiate before Hunter signs with another team, Smith declined to comment, maintaining his policy on all negotiations.
With each passing day, there are increasing signs the Twins are ready to part ways with the seven-time Gold Glove winner.
A Chicago Sun-Times report said the Chicago White Sox could have Hunter signed within the week, although Hunter told the Star Tribune he is not close to an agreement with any team.
"I promise you, it won't be this week," he said. "I don't want to think about that while I'm eating turkey. I want to spend the whole weekend relaxing with my family."
Hunter and Reynolds spent Monday evening at the home of Texas Rangers owner Tom Hicks.
Rangers manager Ron Washington flew in from New Orleans to be there with General Manager Jon Daniels, along with Hicks' sons, Alex and Tom Jr.
"That family was first-class," Hunter said. "They're nice people, down to earth, and the food was good, too."
Hunter, who lives outside Dallas in Prosper, Texas, had met previously with Daniels and Washington.
Hunter also has met with White Sox GM Ken Williams, along with Kansas City Royals GM Dayton Moore and manager Trey Hillman.
The Los Angeles Dodgers, meanwhile, are among the teams whose interest in Hunter could hinge on their ability to make other moves, such as obtaining Florida Marlins third baseman Miguel Cabrera.
Hunter declined to list all the teams involved or detail the negotiations.
"It's a life-changing decision, so I'm not going to make it in a rush," he said. "I'm still in listening mode. I'm not leaning toward anybody. Next week a lot of things could change, so you've just got to let everything play itself out."
Hunter did say he'd prefer to sign his new deal before the winter meetings start Dec. 3 in Nashville.
"If it were up to me," he said, "I'd make a decision in the next 10 days."
Hunter rejected the Twins' three-year offer in late August without making a counterproposal. When the Twins had an exclusive 15-day negotiating window with him after the World Series, he tabled the discussions until other teams could make offers.
Even now, with the talks remaining stalled, Hunter said: "I understand. They have other things they need to think about like signing Johan [Santana]."