But speaking to MLB.com on Tuesday afternoon, Hunter said his free agent thought process will pick up steam on the day following the holiday. But if Hunter and the White Sox were close to reaching a multi-year deal by the end of this week, as reported by the Sun-Times on Monday, then Hunter certainly wasn't tipping his hand to such an outcome.
"Not by the end of this week. I know that for a fact," said Hunter on Tuesday, when asked for a timetable of when he may sign a new lucrative deal. "It could be the end of next week, and it's not necessarily with the White Sox.
"I'm actually trying to weigh my options and think about a couple of other things," Hunter added.
Hunter didn't want to go into specifics of the deals being offered or the teams making offers, but he did admit that five teams had made contact. Ever the diplomat, Hunter said all five teams were in the running.
A sixth team could come into the picture, as a baseball source familiar with the situation confirmed Hunter has a meeting scheduled this weekend with the Dodgers.
The All-Star center fielder confirmed his meeting with the White Sox two Sundays ago. He seemed to come away impressed by the conversation and presentation led by general manager Ken Williams, including personalized messages from Jim Thome and the Bulls' Ben Wallace, a free agent acquisition made by Jerry Reinsdorf's NBA franchise prior to the 2006-07 campaign.
"That's good strategy," said Hunter with a laugh of the Wallace message. "And Jim Thome is one of my favorite guys. I've been watching him since he was with Cleveland. He just destroyed the Twins.
"It all was pretty impressive. Kenny put on a show. He did everything I expected, and he wants to win now. There's absolutely no doubt, and I'm looking to win. That's the big thing."
Along with joining a team which is looking for a chance for immediate success, Hunter lists the need to find a good fit for his family as an overriding factor. Hunter can break down the teams all he wants, from top to bottom, and wants to find a place where he's comfortable.
If his family loves the city, Hunter admitted, then that's where he probably would end up going.
"My family has to like the city. My little boy has to like the city," Hunter said. "It's all family for me.
"This really changes day-to-day. Everything could break down to where the team you thought you wanted to be with might not be the team that's around at the end. You have to be patient, see what happens, and it all will fall into place."
Early expectations of the free agent process had Hunter looking forward to going through teams "courting" him. After about one month of courting, Hunter realized the process is much harder than what he imagined.
"I called a couple of guys who have been through this same thing, and I told them it's kind of a headache," Hunter said. "The decision is life-changing, and you don't want to make a quick decision and make the wrong one."
While Hunter's expressed goal is "to not walk the red carpet in Tennessee" at the Winter Meetings, meaning the deal will be done before the start of December, he didn't indicate a final decision was imminent. Hunter mentioned he had teams set up to talk to and there are still some teams out there who he's "kind of waiting it out to see what happens."
Yet, Hunter seemed truly impressed by the addition of shortstop Orlando Cabrera made by the White Sox on Monday. According to the seven-time Gold Glove winner, he will start breaking down the options by Tuesday and think about what he wants to do.
"After the holiday, I'm going full speed ahead, 100 miles per hour," Hunter said.
As for the problems endured in Chicago by Jacque Jones and LaTroy Hawkins, Hunter's friends and one-time teammates in Minnesota, those past issues won't remotely factor into his final decision.
"Two reasons: I'm a different person than those guys, and my game is different than those guys," Hunter said. "And I'm not with the Cubs. It's the White Sox. That's totally different."
Scott Merkin is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.