Sabathia has had since Nov. 14 to mull a six-year, $140 million package from the Yankees, and he left Las Vegas on Monday afternoon without cashing that ticket.
But another offer may be in the works for Burnett, as the Yankees are said to be willing to go beyond the reported four-year, $60 million offer the Braves have put forth, according to reports on ESPN.com and SI.com.
The ESPN report said agent Darek Braunecker and partner Mark Rodgers arrived in Las Vegas on Monday afternoon and are expected to begin full-scale meetings with clubs regarding Burnett starting on Tuesday.
Cashman said that he is ready to greet any player who wishes to talk with the Yankees.
"I'm more than open," Cashman said. "I prefer meeting with players with their agents instead of doing it the other way. You get a better sense of people and it's a better process for me."
In that vein, Cashman said that Sabathia's deliberate process is not hampering the Yankees.
"We're dealing with other free agents at the same time," Cashman said. "We hope to engage some clubs while we're here. Obviously, today is Day 1 and we have needs we have to fill. I can tell you we're not waiting, per se, for CC. We're trying to affect change in our roster in a positive way with quality additions, but it's just been a slow winter so far."
Burnett, who will turn 32 in January, is considered, along with Derek Lowe -- another target of the Yankees -- among the top right-handed starters on the market.
Burnett set career highs in wins and innings pitched in 2008, going 18-10 with a 4.41 ERA in 221 1/3 innings pitched for the Blue Jays.
The New York Post reported that the Yankees also met with free-agent right-hander Ben Sheets on Monday at the Bellagio, though Sheets is considered a secondary choice if the Yankees should strike out on any combination of Sabathia, Burnett or Lowe.
The Yankees also maintain interest in retaining left-hander Andy Pettitte, though the two sides are set apart over a salary issue. Pettitte made $16 million in each of the past two seasons with New York and rejected a one-year, $10 million contract from the Yankees last month.
Cashman said that he had not scheduled a meeting with Pettitte's representatives, Randy and Alan Hendricks, as of Monday afternoon, but noted that was subject to change.
"We're going to stay engaged with these free agents through the entire process and see how it shakes out," Cashman said.