Scioscia is in the final year of a 10-year contract, and the decision to not seek a new contract is his alone, according to the report, which cited major league sources.
Scioscia, 59, is in his 19th season at the Angels' helm. They last made the playoffs in 2014 and last won a postseason series in 2009. In Scioscia's third year as manager, he guided the Angels to a World Series title, beating the San Francisco Giants in seven games in 2002.
One of the game's most likable managers, the former major league catcher was in a playful mood and joked with reporters while sitting in the dugout before Sunday's game. Once he denied the report, Scioscia was eager to change the subject.
Last October, after Los Angeles finished the season at 80-82, Scioscia said he was fine coming back to the Angels on an expiring contract and would be focused solely on 2018. He reiterated that in a text message to ESPN's Alden Gonzalez on Saturday night.
"Nothing has changed since I spoke on this last October," the manager said in the wake of The Athletic report. "I am focused on this year and will talk to Arte [Moreno, Angels owner], John [Carpino, Angels president] and Billy [Eppler, Angels general manager] after the season."
Eppler declined to comment to ESPN.
The Angels are 55-57 and sit in fourth place in the AL West, 15½ games behind the first-place Houston Astros.
Scioscia is the longest-tenured MLB manager. San Antonio Spurs coach Gregg Popovich (21 seasons) is the only active head coach in the NBA, NFL or NHL with a longer run with a team.
There have been 111 other full-time MLB managers hired since Scioscia's run with the Angels began in 2000, a total that jumps to 131 when including interim managers. The Miami Marlins have had nine managers in that span, the most of any team. Adrian Beltre and Bartolo Colon are the only active players from 2000 who remain in the majors today.
The Athletic said it wasn't clear whether Scioscia would want to manage another team starting in 2019 or if he'd take time off before pursuing another opportunity.
Indians manager Terry Francona said he spoke with Scioscia after seeing the report.
"I just wanted to let him know that I was thinking about him," Francona said. "Because he's going to have to deal with that now."
Scioscia has twice been named AL Manager of the Year. He has managed the Angels in 3,028 games since taking over in 2000 after one season at Albuquerque in the Pacific Coast League.
Only four managers -- Connie Mack (50), Walter Alston (23), Bobby Cox (21) and Tommy Lasorda (21) -- have managed one team for more consecutive seasons than Scioscia. All four are in the Hall of Fame.
Francona said Scioscia's steadiness is remarkable in a game where change is inevitable. Also, Francona marvels at Scioscia's ability to keep his players motivated throughout the years.
"It is really amazing," Francona said. "From my own personal experience, I worry about shelf life. Not worried because you're losing your job. I don't think I've ever worried about that. I worry that, because if your message stops getting listened to, that's not good. And you can't change who you are."
Information from The Associated Press was used in this report.