Street, 33, has been sidelined by the knee issue since Aug. 2. He's been limited to 26 appearances this season, going 3-2 with nine saves and a 6.45 ERA, a 1.93 WHIP and a 1.17 strikeout-to-walk ratio. He also missed 32 games in April and May because of a strained left oblique muscle.
Street is set to earn $9 million next season and has a $10 million club option for 2018 ($1 million buyout).
The Angels have used Fernando Salas in the closer's role in Street's absence.
Austin Laymance is a reporter for MLB.com based in Los Angeles. This story was not subject to the approval of Major League Baseball or its clubs.