Asked if the A's had made an offer for Furcal, Kinzer said, "Not yet."
Asked the same question regarding the Giants, Kinzer paused for a few moments and said, "I don't want to say that, but I will say their interest is very, very strong."
Kinzer added that the A's level of interest is on par with that of the Giants, noting that he talked to Oakland officials last Thursday and Friday.
"The A's have been [interested] all along, and it's been very strong on their part, too," Kinzer said, adding that Furcal, the top shortstop on the open market, might agree to a deal before the Winter Meetings in Las Vegas, Dec. 8-11.
"It could be fairly soon," Kinzer said. "We're hoping to narrow it down to three teams here pretty soon and see where [Furcal] wants to go from there."
Calls to A's general manager Billy Beane and Giants director of player personnel Bobby Evans on Monday morning were not immediately returned.
Kinzer, who called reports that his client is looking for at least four years at $10 million per season "in the ballpark," listed security and "where Rafael feels comfortable" as the top factors in negotiations.
Furcal, 31, appears to be comfortable with the direction of both Bay Area teams.
"He has no problem with the West Coast," Kinzer said of Furcal, who made a reported $13 million in 2008, the final year of a three-year, $39 million deal with the Dodgers. "He's played there and likes it there, and he likes [the A's and Giants]."
The Dodgers and Cardinals are among the teams also said to be interested in Furcal, who missed most of last season with a back injury. He went on the disabled list in early May, had surgery in July and didn't return to the Los Angeles lineup until late September.
The 2000 National League Rookie of the Year and a 2003 NL All-Star with the Braves, Furcal batted .357 with a .439 on-base percentage, five home runs and 16 RBIs in 36 games in 2008, the first season since 2001 in which he played fewer than 138 games.