Brock Lesnar appears to be on his way back to WWE SmackDown.
As pointed out by Wrestling Inc.'s Raj Giri, Lesnar is currently being advertised for several SmackDown tapings from late February onwards. He is currently being promoted for Raw saws up to 21 February, when the red band hits Columbia, South Carolina, but is only scheduled for SmackDown between then and WrestleMania at the moment.
This suggests that the reigning WWE Champion could be on his way back to the blue brand. "Card is subject to change" is an eternal disclaimer in WWE, of course, and there's every chance the promotion will flip Lesnar's schedule around between now and the shows.
Current reporting points towards Lesnar facing Roman Reigns at WrestleMania 38. Brock is currently on deck to defend the WWE Championship against Bobby Lashley at Royal Rumble 2022, while Reigns, the Universal Champion, is wrestling Seth Rollins. As whoever wins the Royal Rumble will be due a title shot at 'Mania, one of Lesnar or Reigns will have to drop their current strap between now and April.
WWE still has Elimination Chamber 2022 between 'Mania and the Rumble. This year will see WWE take that show to Saudi Arabia for the first time, doing so 19 February.