Robinson and Tyson join goalkeepers Frank Fielding and Adam Legzdins, defenders James O'Connor and Tom Naylor and midfielder James Bailey on the transfer list at Pride Park.
All seven players are under contract for at least another year but have been told by manager Nigel Clough that they do not feature in his future plans.
"As is normally the case at the end of the season we've sat down and reviewed where we're at and what we need moving forwards, and we don't see the seven lads featuring on a regular basis," Clough told the club's official website.
"It's nothing personal and there's been no fallings out or anything like that, but we have to be honest and we don't see them figuring in our plans at this moment in time.
"They want to be playing first-team football as well and we have to be fair to them on that front, rather than keeping them hanging around on the off-chance we might have an injury or suspension in their particular area of the team."
Four of the seven have been out on loan this season.
Robinson had three months at Huddersfield and Tyson spent the second half of the campaign at Millwall. They last started a game for Derby at Charlton on December 29.
Bailey has been at Coventry all season and Naylor has had spells at Bradford and non-league Grimsby.