The two-time NL Cy Young Award winner made $13.1 million last season, completing a two-year deal worth $23.2 million.
The highest figure ever asked for in arbitration is $22 million, submitted by Houston pitcher Roger Clemens in 2005 after he became a free agent and accepted arbitration. Among players with less than six years of major league service, the high of $18.5 million has been held by Yankees shortstop Derek Jeter since 2001.
San Francisco figures to give Lincecum the highest offer for an arbitration player, topping the $14.25 million the Yankees submitted for Jeter.
Most players settle before a hearing -- Jeter agreed to a $189 million, 10-year contract, and Clemens accepted a one-year deal for $18,000,022.
Others set to swap figures Tuesday include NL Cy Young winner Clayton Kershaw and Los Angeles Dodgers teammate Andre Ethier, Philadelphia pitcher Cole Hamels, World Series star Mike Napoli of Texas and Chicago Cubs pitcher Matt Garza.
Also in arbitration are three former free agents who accepted offers from their old teams: Boston Red Sox designated hitter David Ortiz, Milwaukee reliever Francisco Rodriguez and Toronto second baseman Kelly Johnson.
San Diego has the most players who filed with 11. The Chicago White Sox are the only team without any.
Lincecum is 69-41 with a 2.98 ERA in five major league seasons and in 2010 helped the Giants win their first World Series title since 1954. He would be 29 when he becomes eligible for free agency after the 2013 season.
While he was just 13-14 last year, his 2.74 ERA was fifth-best in the NL. The Giants scored no runs while he was in the game in seven of 33 starts, had one run six times and two runs five times, according to STATS LLC.
Atlanta outfielder Martin Prado became the first player who filed to reach an agreement, getting a $4.75 million, one-year deal.
Three players who had been eligible for arbitration agreed to one-year contracts: Phillies right-hander Kyle Kendrick ($3,585,000), Boston Red Sox outfielder Ryan Sweeney ($1.75 million) and Pittsburgh right-hander Chris Resop ($850,000).
In a trade Friday night, the Seattle Mariners sent hard-throwing right-hander Michael Pineda and 19-year-old righty Jose Campos to the New York Yankees for power-hitting catcher Jesus Montero and 24-year-old pitcher Hector Noesi.
The Yankees also agreed to a one-year, $10 million free-agent contract with right-hander Hiroki Kuroda. The 36-year-old Kuroda can also earn performance bonuses as part of the deal.
Among other free agents, reliever Kerry Wood is remaining with the Chicago Cubs. He agreed to a one-year, $3 million contract for 2012 with a $3 million club option for 2013. Shortstop Jack Wilson decided to stay with the Braves for a $1 million, one-year deal.