Across San Francisco Bay, the Oakland Athletics also are courting Furcal.
Furcal's agent, Paul Kinzer, said Monday the Giants and A's are still serious contenders to sign Furcal.
"Yes, they are," Kinzer said in a telephone interview. "Right now we still have four teams we're talking to."
Kinzer also said a report in the El Caribe newspaper in Furcal's native Dominican Republic that Oakland had made Furcal an offer for $48 million over four years "wasn't true" and added that he had not been in contact with the New York Mets about Furcal's services.
The 31-year-old Furcal has played the past three seasons with the Los Angeles Dodgers, so he is familiar with the NL West. That's after he spent his first six major league seasons with the Atlanta Braves.
He was limited to 36 games last season and activated from the 60-day disabled list during the final week after being sidelined since May 6 with back problems. He hit .357 with five home runs and 16 RBIs for the division champions, who swept the Chicago Cubs in the first round of the playoffs then lost in five games of the NL Championship Series to the eventual World Series champion Philadelphia Phillies.
Renteria, 33 and a 13-year big league veteran, batted .270 with 10 homers and 55 RBIs this year for the Detroit Tigers. Last month, Detroit declined its $11 million option for Renteria and gave him a $3 million buyout.
Giants general manager Brian Sabean said just after the 2008 season ended there was "zero" chance the club would re-sign the 41-year-old Vizquel despite his popularity, positive clubhouse influence and ever-reliable defense even for his age and after undergoing left knee surgery during spring training.
Committed to developing its young player, San Francisco had been grooming speedy rookie Emmanuel Burriss as Vizquel's successor, but adding a veteran such as Furcal or Renteria would allow Burriss additional time to grow into the position.
New Giants owner Bill Neukom, who took over for now-retired managing partner Peter Magowan on Oct. 1, instructed Sabean and manager Bruce Bochy to go after the top players available this winter with Neukom ultimately deciding whether the club could actually afford to sign them.
San Francisco hasn't reached the playoffs since 2003, didn't play well at home this year and lost the buzz it had during the 2007 season with Barry Bonds' home run chase and the All-Star Game in town.
The Giants need someone they can count on in the middle of the infield, especially if the rest of the spots are filled by less-experienced players. Some offensive punch wouldn't hurt either.
Vizquel was limited to 92 games in 2008 -- his fewest since playing 64 in 2003 for the Cleveland Indians, the second-to-last year of his 11-season tenure there. Vizquel batted .222 with 23 RBIs, 10 doubles and a triple in 2008.
Oakland, meanwhile, has former first-round pick Bobby Crosby under contract through 2009 but innovative GM Billy Beane might look to trade him as he's done with so many others recently, especially considering Crosby is due to earn $5.25 million next season. Until this year Crosby had been plagued by injury and hadn't been the same since his 2004 Rookie of the Year season.