The Athletics offered Giambi, who is eligible to become a free agent in November, a six-year contract worth more than $90 million during the season, but were not willing to give him a no-trade clause and that caused negotiations to cease.
However, Athletics general manager Billy Beane told the San Francisco Chronicle that the organization is now prepared to give Giambi a no-trade clause.
"We've told Jason and (Giambi's agent) Arn Tellem, that's (no-trade clause) no longer an issue," Beane told the newspaper.
Giambi, who turns 31 in January, is the key offensive player on a young A's team that won 102 games -- second most in the majors -- but squandered a two games to none lead and lost to the New York Yankees in the American League Division Series.
Ironically, the Yankees may make a bid for Giambi, who has made no secret of his fondness for New York and the Yankees' tradition. But he is also the leader of the A's and Beane believes he may be able to retain Giambi.
"I'm optimistic," Beane said in the San Francisco Chronicle. "We have a good relationship, so there's trust and good feeling in the negotiations."
Giambi can very well earn a second straight Most Valuable Player Award after batting .342 with 38 home runs and 120 RBI. He ranked first in the league in slugging percentage (.660), doubles (47) and walks (129), second in batting behind Seattle's Ichiro Suzuki, sixth in runs (109), seventh in homers and eighth in RBI.
When he captured the MVP honor in 2000, Giambi hit .333 with 43 homers and 137 RBI and ranked third in slugging percentage (.647).