Kevin Feige is reportedly not going to be taking over Lucasfilm. According to Variety, their sources tell them that the Marvel Studios President is "fully committed with his Marvel duties and has no ambition to lead Lucasfilm or take more of a role."
It was announced in September 2019 that Feige will be producing a Star Wars movie, which sparked speculation that the MCU head would be a bigger part of the Star Wars universe moving forward. Kathleen Kennedy is currently the President of Lucasfilm.
Details on Feige's Star Wars movie are non-existent at the moment, and he recently confirmed to Entertainment Weekly that he wouldn't be involved with Lucasfilm's live-action Star Wars spinoffs. "No. That's all Kathy Kennedy," Feige commented. "I'm involved in as much as I stay up until midnight L.A. time to watch new episodes of The Mandalorian when they drop."
The news that Feige is sticking with Marvel doesn’t come as much of a surprise, seeing as Feige seems to have his hands full with the MCU. Marvel's Disney Plus rollout got off to a huge start with WandaVision and The Falcon and the Winter Soldier, and will continue next month with the highly anticipated Loki. On the movie side, Black Widow will finally debut this July after a series of pandemic-induced delays, and Shang-Chi and the Legend of the Ten Rings, Eternals, and Spider-Man 3 will all land this year as part of Marvel Phase 4, too.
As for Star Wars, The Book of Boba Fett is due for release this December, and Obi-Wan Kenobi, The Mandalorian season 3, Andor, and Ahsoka are all among the live-action projects in the pipeline.