Braunecker characterized the outside interest in Lee as "strong" and said that there were a "significant number of clubs that are interested at varying levels."
Both the Rangers and Yankees have acknowledged meeting with Lee face-to-face this offseason in Arkansas, but Braunecker said that there have been meetings in person with other undisclosed clubs as well.
"To me, you're talking about the best player on the market," Braunecker said. "There's still certainly a need for starting pitching out there that extends beyond the clubs that have been mentioned at this point."
Braunecker said that the negotiations for Lee are "about where we anticipated" as teams prepare to do business at the Walt Disney World Swan & Dolphin Resort.
With Lee the unquestioned star of the show, Braunecker said his client might find a deal to be made before the end of the Winter Meetings on Thursday, but nothing is guaranteed.
"I wouldn't be surprised either way," Braunecker said. "We're in the process. We're going to be meeting a lot of people. We're just getting things rolling."
The Yankees have identified Lee as their top priority outside the organization, with some suggestions that they could dig in for a package that approaches the $23 million per season that CC Sabathia -- the game's highest-paid pitcher -- is earning.
"It's their dance card," Yankees general manager Brian Cashman said. "They're setting the pace of this thing. I can only wait and respect the process they put themselves in. It took them a long time, they fought through a lot of different cities to get to this point. I'm hoping this will be the last city he ends up in -- in New York. We'll see how it plays out."
Rangers club president Nolan Ryan has acknowledged his team may be unable to outbid the Yankees, but the Rangers are still pushing hard to retain Lee, who helped carry the club to its first World Series this past year.
Braunecker said that the Rangers' proximity to Lee's home in Little Rock, Ark., will be a factor, but just one of many that will be considered during the course of the negotiations.
"It's one of the variables he's going to have to consider," Braunecker said. "Obviously, they're the closest club to Little Rock, and proximity to home is a factor for anybody that goes through this process. To what degree, I don't know. I guess we'll figure that out as the process continues to evolve."
Braunecker added that the visit by Cashman in November was "very favorable" and that it allowed him to personalize the organization beyond Lee's experiences at Yankee Stadium and in New York.
"Cliff has clearly demonstrated he can pitch in any market," Braunecker said. "When you think about it, he's gone from Cleveland to Philly to Seattle to Texas. He hasn't had a hiccup in any of them."
Though Braunecker figures to be a heavily sought person during the Winter Meetings, he said that Lee is content allowing his agent to handle the negotiations, only asking to be kept informed of new developments.
"That's the extent of it," Braunecker said. "When there's something substantive, I report back to him. Otherwise, he's on a deer-hunting excursion right now. He's probably having a lot more fun doing that."
Bryan Hoch is a reporter for MLB.com. T.R. Sullivan is a reporter for MLB.com. Read his blog, Postcards from Elysian Fields and follow him on Twitter @Sullivan_Ranger. This story was not subject to the approval of Major League Baseball or its clubs.