Sure, but that will be the most broken rule in history. Contracted players will get to the end of the season and suddenly happen to want to start discussions with a different club.As I say, I think now it should apply only to contracted players, especially first year draftees like JH-F.
Similarly clubs shouldn't be allowed to offer contracted players as a potential trade throughout the season either.
You're trying to unpick a much bigger problem IMO: some clubs are more desirable than others, and we don't give young players a choice (and fair enough). I think that if you make it a longer contract to start with, then at least clubs have a bigger bargaining chip after just one year.