"We are in the infancy stages," Lee's agent, Darek Braunecker, told ESPNNewYork.com.
Braunecker said that he heard from "multiple" teams on Sunday when free agency began, but declined to go into specifics.
While the Yankees have identified Lee as their No. 1 free-agent target, the Texas Rangers' organization made a positive impression on Lee after acquiring him in July. Texas is closer to Lee's Arkansas home and it has no state tax.
It is believed that negotiations will start with Lee asking for a contract that matches CC Sabathia's seven-year, $161 million deal. Braunecker declined comment.
The process is likely to last over the next month, extending to the winter meetings in Orlando, Fla., in early December. Since there are no other market factors, Lee can take his time, feeling confident that being patient won't hurt him.
Unless a potential ace becomes available at next week's GM meetings, also in Orlando, it doesn't appear that there is anyone on the trade market that could bump a team out of the Lee sweepstakes. The Kansas City Royals will listen on Zack Greinke, but a baseball official with knowledge of the Royals' thinking said Kansas City needs to be overwhelmed to make a trade.
A club like the Yankees will not do that unless it knows it is not going to acquire Lee. Greinke might not be a good fit for New York anyway. He reportedly has the Yankees on his no-trade list and his personality might not work in the pressure of the Bronx.
Lee, 32, has already proved that he can handle the postseason, which is why the Yankees and Rangers figure to fight to the last dollar for him. He is 7-2 with a 2.13 ERA in the playoffs.
Having pitched in both leagues, Lee is very familiar with his potential future home ballpark. He may take trips to visit with teams, but it will be a case-by-case process, Braunecker said.
It will not be a quick process, but by this time next month, the day the winter meetings end, Lee will likely have found his home.
"When the time is right, when we get the right deal, we will act," Braunecker said.
Andrew Marchand covers the Yankees for ESPNNewYork.com.