A source with knowledge of the situation said that Sabathia is likely waiting to see if a West Coast team will become involved before he makes a final decision.
However, following the meeting with Sabathia and agent Greg Genske, Girardi said that his sense was that Sabathia was "absolutely" interested in New York.
"I just think, when I look at CC, I look at a guy that has three young kids and he's trying to make the decision that is best for his family," Girardi said. "He's not going to rush into it. You wait a long time to become a free agent and there's no reason to jump the first week, just like every player does."
It is known that Sabathia would prefer to play close to his Vallejo, Calif., home and in the National League, having enjoyed his experience being able to bat without the designated hitter rule in place after joining the Brewers in-season this year.
The Brewers have offered Sabathia a five-year commitment in the $100 million range, and the Chicago Tribune cited sources Monday indicating that the Brewers had already added a sixth year to their initial proposal.
According to that report, general manager Doug Melvin was "considering a willingness" to add a clause that would give Sabathia the opportunity to opt out after three seasons. In that scenario, Sabathia could be a free agent again in the 2011-12 offseason as a 31-year-old.
With the otherwise occupied Dodgers and Angels unlikely to become involved, it is thought that the Giants could be Sabathia's last hope for scoring a California club.
San Francisco has discussed parameters with Sabathia's agent, Greg Genske, but no official offer has been made. The Giants could be prepared to top Milwaukee's offer, but will not approach New York's outlay. A package in the range of $120 million could be possible, even with the Giants' busy winter to date.
That might be enough to convince Sabathia, who resides approximately 30 minutes from San Francisco. While co-chairman Hal Steinbrenner has cautioned that the Yankees' offer will not be there forever, the club has no immediate designs on issuing a deadline.
It is expected that Sabathia -- who came to Las Vegas to watch Saturday's fight between Manny Pacquiao and Oscar De La Hoya -- will meet with both the Brewers and Red Sox before leaving for home on Monday.
Cashman is expected to address reporters in a 6 p.m. ET interview session at the Bellagio hotel. The Yankees are also known to have varying levels of interest in other players being discussed during this week's Winter Meetings, including pitchers A.J. Burnett and Derek Lowe, plus sluggers Mark Teixeira and Manny Ramirez.