Lincecum is seeking the richest contract ever awarded in arbitration, surpassing the $10 million that Alfonso Soriano (2006) and Francisco Rodriguez (2008) got after losing cases and Ryan Howard got after winning his in 2008.
If Lincecum and the Giants don't settle, an arbitration panel will hold a hearing next month and pick one of the salaries.
Lincecum's case is an interesting test because few players have entered salary arbitration with credentials similar to his. Called up early in the 2007 season, the right-hander has a 40-17 record with a 2.90 ERA.
He won the Cy Young in his first two full seasons, becoming the first repeat winner since Randy Johnson from 1999-2002. Lincecum was a bargain for the Giants last year, when he made $650,000.
He had no negotiating leverage then, but is guaranteed to increase his salary by more than twelvefold even if he loses his case because he is eligible for arbitration as a so-called "Super 2" -- a player in the top 17 percent of service time between two and three seasons.
Lincecum's case could be most similar to Howard, whose $10 million request in 2008 had been the highest ever for a player in his first year eligible for arbitration. Howard won the NL MVP in 2006 when he led the league with 58 home runs and followed that with 47 homers in 2007. The Phillies offered $7 million.
Lincecum, nicknamed "The Freak" for his giant stride and slender body, has been the NL's most dominant pitcher almost from his arrival. He has a 33-12 record with a 2.55 ERA the past two seasons, leading the league in strikeouts both years. He has 526 strikeouts during that span, averaging 10.5 per nine innings.
Lincecum also leads the majors in ERA, batting average against (.214), winning percentage (.733) and strikeouts over the past two seasons.
Earlier on Tuesday, Lincecum agreed to pay $513 to resolve marijuana charges against him in Washington state.
He originally faced two misdemeanor charges of marijuana and drug paraphernalia possession stemming from a traffic stop on Oct. 30. The charges were reduced to a civil infraction.
Lincecum appeared in Clark County District Court before Judge Darvin Zimmerman on Tuesday morning. Giants managing partner Bill Neukom was in court in a sign of support for Lincecum.
He paid a speeding ticket separately.