5:15pm: The Giants and Mariners have definitely discussed League, according to Jon Paul Morosi of FOX Sports (on Twitter). It's still not clear where League will be traded, though, according to Morosi.
4:06pm: The Mariners were discussing League with multiple teams as of this afternoon, Jon Paul Morosi of FOX Sports reports (on Twitter).
3:03pm: There's some scuttlebutt in high circles that the Giants are the team getting League, Henry Schulman of the San Francisco Chronicle reports (on Twitter). But it's not a sure thing.
2:52pm: The Braves and Rangers aren't in the mix for League, Crasnick tweets.
2:46pm: The Angels and Mariners are in talks for League, Alden Gonzalez of MLB.com reports. The Mariners could be close to trading League to the Giants or the Angels, Gonzalez writes.
2:05pm: The Mariners are close to trading Brandon League to an unknown team, ESPN.com's Jerry Crasnick reports (on Twitter). The Giants, Angels and Mets are known to have some interest in the right-hander.
League is earning $5MM this year and will hit free agency this offseason. The 29-year-old has a 3.05 ERA with 5.3 K/9, 3.9 BB/9 and a 46.4% ground ball rate in 42 1/3 innings for Seattle. He lost the closer's job in May, but has pitched to a 1.96 ERA with twice as many strikeouts as walks since the beginning of June. His fastball averages 95.2 mph, according to FanGraphs.
Steve Adams contributed to this post.