‘The Freak’ is looking to cash in with the Giants. (Jeff Chiu/AP)

Now the two-time National League Cy Young award winner wants to be paid like it.

The 25-year-old right-hander asked his team for $21.5 in salary arbitration Tuesday — a notable bump up from the $17 million the Giants put on the table.

San Francisco’s offer is the highest ever, exceeding the $14.25 million the New York Yankees offered to star shortstop Derek Jeter in 2001. The largest ever proposed arbitration number from a player came from Roger Clemens, who in 2005 asked the Houston Astros for $22 million. Lincecum earned $13.1 million last season in the final season of a two-year contract, a deal finalized before Lincecum’s arbitration hearing before the 2010 season.

“I’m optimistic that we’ll find common ground without a hearing room,” Giants vice president of baseball operations Bobby Evans said before seeing Lincecum’s request. “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 has been the linchpin to San Francisco’s top-notch rotation over the last several years, compiling a 69-41 career record with a 2.98 ERA and 9.9 strikeouts/9 innings ratio. But the man they call ‘The Freak’ could use a little more support from his teammates. Despite a 2.74 ERA in 2011, Lincecum finished with his first losing record (13-14). In seven of his 33 starts the Giants produced zero runs, while in 11 others they managed only one or two, according to STATS LLC .

One key cog in the Giants’ sometimes-anemic offense is third baseman Pablo Sandoval, who on Tuesday agreed to a three-year, $17.15 million contract to stay by the bay. Sandoval dropped nearly 40 pounds before last season and it paid off in the form of a .315 average with 23 home runs and 70 RBIs and an All-Star nod.

The Giants also avoided arbitration with outfielders Melky Cabrera and Nate Schierholtz and relief pitcher Santiago Casilla by signing all three to one-year contracts. The Giants also agreed to a one-year, $4.85 million deal with outfielder Angel Pagan. The team expects to have a payroll around $130 million this season.

In all, 79 players agreed to contracts across the league on Tuesday while 54 others exchanged arbitration numbers with their respective teams.

More MLB news from Washington Post Sports:

Linceum offered $17M by Giants, asks for $21.5M

Giants sign Angel Pagan to $4.85 million, one-year deal

Players, teams start rush to settle salary arbitration cases