Marvel Studios and Disney are apparently planning to start production on Loki season 2 in 2022. That hint about Loki's sophomore season comes from a Production Weekly, which has a listing for the Disney+ series to begin shooting season 2 at that time. That production update corroborates the earlier rumors from this year, where Marvel insiders dropped the scoop that Loki was already slated for a second season run. The timing of that start on Loki season 2 could also point to when Marvel Studios plans to premiere Loki season 1 on Disney+, following the delays of the COVID-19 pandemic.
Murphy's Multiverse reports that Loki star Tom Hiddleston also has obligations to his upcoming Netflix series White Stork, which is slated to begin filming in March 2021 in the UK, for 2022 release. Hiddleston was already filming Loki season 1 when the coronavirus pandemic hit; provided he can finish that production before March 2021, it would then make sense for Loki to premiere on Disney+ in the summer/fall range, with season 2 possibly going back to the launch window of January/February 2023.
If not for the pandemic, Loki was expected to help kick off 2021 for Marvel and Disney+ - now we're just hoping to get WandaVision late this year or early next year, while The Falcon and the Winter Soldier has long since missed its original fall premiere date, with no certain revised premiere date yet announced.
The Loki Disney+ series will follow the version of Hiddleston's Asgardian trickster who escaped from the alternate 2012 timeline (using the Tesseract) during the "Time Heist" portion of Avengers: Endgame. With Loki 2012 now considered a major anomaly in the Marvel Cinematic Multiverse, we will meet new factions like The Time Variance Authority. From what (little) we've seen of Loki, the series will seemingly be framed as an interrogation, with Loki having been arrested by the TVA for some unknown offense across the timelines - which we'll presumably learn more about in flashback. There has also been a hint that the new MCU big bad Kang The Conquerer (Jonathan Majors) will at least get first mention as part of Loki's storyline. Similarly, fans are eager to see how Loki hopping through the Multiverse connects back to the other Phase 4 storyline being explored in WandaVision, Doctor Strange in the Multiverse of Madness - and possible Spider-Man 3, as well.
Loki season 2 will start production in 2022; season 1's premiere date has yet TBA.