The two-time NL Cy Young Award winner was among 54 players who exchanged figures with their teams, and his request fell short of the record $22 million requested by Roger Clemens from Houston when he became a free agent and accepted the Astros' arbitration offer before the 2005 season.
Interrupting the frenzied focus on money, there were two notable injury announcements.
Detroit said star slugger Victor Martinez could miss the entire season after tearing his left anterior cruciate ligament last week during off-season conditioning.
"After you feel sorry for yourself for a day or so, you move on," general manager Dave Dombrowski said. "We have a good club. We've got a lot of players who will step up."
Boston outfielder Carl Crawford had surgery on his left wrist Tuesday and could miss opening day. He was bothered by the wrist last season, and felt discomfort as he intensified pre-spring training workouts.
"Carl will be our everyday left-fielder for the bulk of the 2012 season," new general manager Ben Cherington said. "We're not ruling out opening day, but we're not going to put a timeline on it."
At the exchange of arbitration figures, Lincecum set a mark among players with less than six years in the majors, topping Derek Jeter's $18.5 million submission in 2001. And the Giants' offer broke the 11-year-old club mark of $14.25 million offered by the Yankees to Jeter that winter.
"I'm overall optimistic that we'll find common ground without a hearing room," Bobby Evans, Giants vice-president of baseball operations, said before seeing Lincecum's filing numbers. "It's a process that begins long before today in terms of conversations about possible deals that work for both sides. That process has continued in a mutual fashion. At this point we haven't reached a conclusion."
Lincecum is eligible for free agency after the 2013 season.
Boston designated hitter David Ortiz, who became a free agent and accepted Boston's offer of arbitration, had the second-highest request at $16.5 million and was offered $12.65 million by the Red Sox.
Other large amounts involved Chicago Cubs pitcher Matt Garza ($12.5 million vs. $7.95 million), Philadelphia outfielder Hunter Pence ($11.8 million vs. $9 million), Texas World Series star Mike Napoli ($11.5 million vs. $8.3 million), Los Angeles Dodgers NL Cy Young Award winner Clayton Kershaw ($10 million vs. $6.5 million) and Baltimore right-hander Jeremy Guthrie ($10.25 million vs. $7.25 million).
Garza's $4.55 million gap was the largest. All-star pitchers Chris Perez of Cleveland and Jair Jurrjens of Atlanta submitted the same figures as their teams, a signal a deal already was all but finalized.
Barring agreements, hearings before three-arbitrator panels will be scheduled for the first three weeks of February. Players won two of three hearings last winter, but teams lead 286-212 since arbitration began in 1974. The 119 players in arbitration averaged a 121 per cent increase last year, according to a study by The Associated Press.
Among the 142 players who filed last Friday, 98 already have settled, including 10 after figures were exchanged.
There was just one multiyear agreement among Tuesday's deals, with Giants third baseman Pablo Sandoval getting a $17.15 million, three-year contract, a deal subject to a physical.
The largest one-year deals went to Philadelphia pitcher Cole Hamels ($15 million), Dodgers outfielder Andre Ethier ($10.95 million), Boston outfielder Jacoby Ellsbury ($8.05 million), Milwaukee reliever Francisco Rodriguez ($8 million), San Diego outfielder Carlos Quentin ($7,025,000) and Tampa Bay outfielder B.J. Upton ($7 million).
Among international free agents, the Milwaukee Brewers agreed to a two-year contract with Japanese outfielder Norichika Aoki, a three-time batting champion in Japan's Central League.
Texas had a deadline of 5 p.m. ET on Wednesday to reach an agreement with Japanese pitcher Yu Darvish.
Also, former all-star pitcher Joe Saunders agreed to a $6 million, one-year contract with Arizona, which cut him loose last month rather than allow him to become eligible for arbitration.
AP Baseball Writer Janie McCauley and AP Sports Writers Jimmy Golen and Noah Trister contributed to this report.