The San Jose Mercury News reported on Tuesday that Sabathia's team and Giants representatives met on Monday night and were planning on meeting again after the winter meetings.
That would preclude a quick resolution to the New York Yankees' reported six-year, $140 million offer to the left-hander.
Los Angeles Dodgers general manager Ned Colletti said on Monday that Sabathia told him that he wants to be a Dodger, but the team has not publicly made an offer.
Sabathia grew up in Southern California and has been building a home there. In the past he has expressed a desire to play for a West Coast club. In their first season without Barry Bonds, the Giants posted a 72-90 record and finished fourth in the National League West.