If Street undergoes surgery on his inflamed right knee, the Angels are confident the right-hander would be able to pitch in 2017.
"I haven't heard anything in the first couple evaluations of the knee that says it would be any kind of major surgery," Scioscia said. "All surgery has some unknown quantity as far as how guys come back. I think what has been talked about with Huston would be of the minor surgery variety."
Street, 33, has 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's been on the 15-day disabled list since Aug. 2. 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 will continue to mix and match relievers in the closer's role with Street out indefinitely.
Cam Bedrosian got the first crack at earning the closer job when Street landed on the DL, but Bedrosian was injured in his second outing after the Angels lost Street. Bedrosian has been on the DL since Aug. 9 with right middle finger flexor tendinitis. He began a throwing program this week, but has since been shut down and will be evaluated on Monday.
"Cam is going to be evaluated tomorrow, and I think he's feeling much better, but maybe not quite where you would hope to," Scioscia said. "He started to throw, and I think first and foremost, it feels much better, but not quite where he's ready to get back out there and get after it and get on the mound. Progress has been slow, but we'll get more answers in the next couple days."
• The Angels optioned first baseman/outfielder Ji-Man Choi to Triple-A Salt Lake and recalled right-handed reliever A.J. Achter from Salt Lake before Sunday's series finale against the Yankees.
Choi had not played since Thursday, with the Angels using Nick Buss in left field and C.J. Cron coming off the disabled list on Saturday to resume his role as the primary first baseman. The Angels want Choi to get regular at-bats in the Minors, and could bring him back to the Majors when rosters expand Sept. 1.
"We need pitching right now," Scioscia said. "He'll get more regular at-bats and hopefully improve as much as he did the first time down. I think he's making strides towards where he needs to be, but it's not going to happen unless you play every day, and he needs to get everyday at-bats."
Austin Laymance is a reporter for MLB.com based in Los Angeles. He covered the Angels on Sunday.