Good luck with that. They can not be local players as that would cause problems with regulations on national team level as well with players playing at an other countries national team etc...
In Football, countries already have some own regulation on what counts as own player. For example in the Premier league a home grown player counts as home player even though he is foreigner but he qualifies for the certain rules (get to the club before certain age, spent their certain years etc) So I can imagine Turkey might try to qualify for something like this with a few players but I can not see yet any sport federation changing these rules. That would have too much consequences on other rules and regulations.
Ah! I didn't really mean local actually. They keep playing in their own nationalities but as EU citizens so they don't count as one of the foreign players. I think in Spain, football teams have such a regulation where you can only have 4 players out of EU. I'm sure if the football federation allows that it will be an example to other sports as well.