The San Francisco Chronicle reported earlier Thursday that, according to a major league source, the Giants have made a three-year, $37 million offer to the two-time Cy Young Award winner, with annual salaries of $9.5 million, $12.5 million and $15 million.
The newspaper reported that Lincecum's camp responded with an offer worth more than $40 million.
However, baseball sources told Olney that as of noon ET Thursday, the two sides were not close to a deal.
Wednesday, multiple outlets reported Lincecum's arbitration hearing is scheduled to be held Friday in St. Petersburg, Fla. The Giants filed for $8 million while Lincecum countered with $13 million. He earned $650,000 last season.
Lincecum, the reigning National League Cy Young winner, was 15-7 last season with a 2.48 ERA. He's 40-17 in his three major league seasons with a 2.90 career ERA.
Still scheduled for arbitration hearings as of Thursday were: Brewers outfielder Corey Hart, Los Angeles Angels shortstop Erick Aybar, Washington right-hander Brian Bruney, Nationals left-hander Sean Burnett, Baltimore right-hander Jeremy Guthrie, Arizona right-hander Edwin Jackson, San Francisco right-hander Tim Lincecum, Angels catcher Jeff Mathis, Houston left-hander Wandy Rodriguez, Florida outfielder Cody Ross, Chicago Cubs shortstop Ryan Theriot and Tampa Bay outfielder B.J. Upton.
Information from ESPN The Magazine senior writer Buster Olney and The Associated Press is included in this report.