Variety was first to report the news. NBC had no comment when reached by ET.
Davidson joined SNL in 2014 at age 20, making him one of the youngest stars to join the cast in the show's history and rose to fame with characters like Chad.
He's notably made fewer appearances during the current season amid his romance with girlfriend, Kim Kardashian, who hosted a 2021 episode of the series.
"Kim and Pete are doing great," a source told ET of the couple earlier this month. "She definitely foresees a strong, healthy and promising future with him. He is so respectful of her and treats her like an absolute queen. He is completely enamored by her beauty and talent. He thinks she's an awesome mom and would more than likely take their relationship to the next level in a heartbeat, but Kim isn't quite there yet."
"Things between Kim and Pete are easy, seamless and fun," the source added. "They are completely themselves around each other and Kim feels incredibly comfortable, protected and secure when she's with Pete."
SNL is set to wrap its 47th season on Saturday, with host Natasha Lyonne and musical guest Japanese Breakfast. It's unclear if Davidson will appear on the season finale, as many in the Kardashian circle are heading to Italy for Kourtney Kardashian and Travis Barker's wedding.
Davidson already has his next project lined up; he's set to write, star and executive produce Bupkis, a live-action, half-hour comedy that will be "a heightened, fictionalized version" of his real life.