Greinke met with the Dodgers on Thursday, but it is not known when he got together with officials from the Angels. Greinke, who finished last season with the Angels, has been in Southern California in the past few days.
According to reports, Greinke has other suitors, including the Texas Rangers and Washington Nationals. It is not known whether he will meet with those clubs before Monday's winter meetings get under way in Nashville, Tenn.
The Dodgers' deep financial resources -- they are reportedly closing in on a new long-term TV deal that could net them $6 billion or more over 25 years -- could make them difficult to outbid for Greinke.
The Dodgers said shortly after the season that their No. 1 priority this winter was to add at least one premier starting pitcher. Reports have suggested Greinke could fetch a record contract for a right-handed pitcher, perhaps in the neighborhood of six years and $150 million.
Greinke, the 2009 AL Cy Young winner, is 91-78 with a 3.77 ERA lifetime. He was 6-2 with a 3.53 ERA for the Angels last season after being traded from Milwaukee. He was 9-3 with the Brewers and finished the 2012 season 15-5 overall with a 3.48 ERA.
The Dodgers also have checked in on free-agent right-hander Kyle Lohse, according to a source. Earlier this winter, the Dodgers submitted the highest bid for left-hander Ryu Hyun-jin, and they have until Dec. 10 to work out a contract or Ryu will return to pitch in his native South Korea.