Garciaparra, 32, also is considering the New York Yankees, Cleveland Indians and Houston Astros, but the Dodgers might have an advantage because Garciaparra and his wife, former soccer star Mia Hamm, live in suburban Manhattan Beach.
"Nomar continues to talk with players, friends and family members," Garciaparra's agent, Arn Tellem, said in an e-mail Friday. "He is weighing his options carefully and while he has no plans on making a decision today, he intends to do so in the near future."
Garciaparra and Tellem met Thursday with Dodgers owner Frank McCourt, general manager Ned Colletti and senior vice president Tom Lasorda.
"We met again today. He came out again today with Mia," Colletti said on a conference call late Friday. "I can tell you from my perspective both meetings were very good. They took the time to come out here two days in a row."
Colletti told reporters Wednesday he had made an offer to Garciaparra. When asked if he was optimistic, Colletti replied: "I don't have any comment on that. I don't get optimistic until a player signs. Too many things happen."
Colletti also said he had no idea which teams might be in the competition for Garciaparra and he had received no indication as to when Garciaparra would reach a decision.
"I need to find a player who can hit in the middle of the lineup," Colletti said, adding Garciaparra would fill that need.
Garciaparra played under recently hired Dodgers manager Grady Little in 2002-03 with the Boston Red Sox and was teammates with pitcher Derek Lowe and third baseman Bill Mueller in Boston. Lowe signed with Los Angeles last winter, and Mueller joined the Dodgers this week.
Garciaparra was considered one of baseball's best shortstops for several years while playing with the Red Sox, but his playing time was limited the past two seasons because of injuries. He was traded to the Chicago Cubs midway through the 2004 season.
Should Garciaparra join the Dodgers, he probably would play first base or the outfield because the team has reached agreements with shortstop Rafael Furcal and Mueller, a third baseman. All-Star Jeff Kent is at second.
Colletti said he discussed different positions with Garciaparra.
"I gave him some of my thoughts, he gave me some of his thoughts," Colletti said. "He was really amenable to doing whatever we needed him to do. He just wanted to know, as most players do, how to prepare."
A five-time All-Star with the Red Sox, Garciaparra hit .283 with nine homers and 30 RBI in 62 games for the Chicago Cubs last season, when he earned $8.25 million. He tore his left groin running out of the batter's box in St. Louis on April 20 and didn't return until Aug. 5.