United recently invested huge amount of money in Hojlund and Zirkzee, I would be surprised if they would be willing to bid for Gyökeres, Amorim coming or not.
They pretty much bought Ten Hag half of his Ajax team, I don't think they will do it again for a young, relatively unproven manager. MU squad has a lot of talent and depth, I think the new manager will have to try cook something out of it, I don't expect a lot of transfers from their side in January.
By the way, he already got Ugarte, he was one if his best player ~1.5 years ago.