It evolves when it reaches Level 28, no stones or items required. If you really wanted a Persian without having to evolve Meowth, go to One Island.
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Meowth evolves into Persian at level 28
Meowth will evolve into a Persian at level 28
it depends if he choose to evolve or not.
Your Meowth will evolve into Persian when it reaches the Level 28. Remember that only Meowth can learn the move "Pay Day", so wait until it learn this before evolving.
get to lvl 40