With ace right-hander Felix Hernandez on the verge of signing a five-year, $78 million contact, which could be finalized and announced as early as Thursday or Friday, the lone remaining salary arbitration-eligible player still unsigned would be first baseman Casey Kotchman.
The Mariners on Tuesday avoided salary arbitration with right-handed relievers David Aardsma for $2.75 million and Mark Lowe for $1.15 million.
League, acquired in a trade with the Blue Jays for right-handed pitcher and former first-round Draft choice Brandon Morrow, made $640,000 last season and submitted a $1.325 million request through salary arbitration while the Mariners offered $900,000.
Kotchman, who made $2.885 million last season while spitting the season between the Braves and Red Sox, is seeking a $3.9 million contract while the Mariners offered $3.135 million on Tuesday.
League, 26, appeared in a career-high 67 games last season with the Jays, posting a 3-6 record and 4.58 ERA. He also had nine holds and 76 strikeouts and compiled a 2.30 ERA on natural grass fields.
He was originally selected by Toronto in the second round in the 2001 First-Year Player Draft out of St. Louis High School in Honolulu, Hawaii. He has appeared in 168 career Major League games, all in relief, going 7-10 with a 4.09 ERA. He has a career ground-ball rate of 3.25 (384 ground balls, 118 fly balls), ranking second-best among relievers since his debut in 2004.
Jim Street is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.