Antonio moved to Hillsborough on loan for the second half of last season and impressed immediately, helping the club gain automatic promotion to the Championship. He is now keen to leave Reading, in order to continue to progress with his career.
McDermott is currently waiting to see if the Owls are going to approach Reading with a new bid.
“There's been an offer, but we've turned it down," McDermott said. "I'm not sure how much we have heard since.
"Michail's view is that there are a lot of players in front of him, so he needs to move on for his career. That's absolutely fine and I understand that. He's training well and working well. We love Michail, so we will see what happens.
"He's in a great environment here working with some really good players and he's always trying to be the best that he possibly can."
Reading will be playing in the Premier League this season, after winning the Championship last season and gaining promotion. Their first game is against Stoke City, at the Madejski Stadium.