Fulham have been rejected in their request to have the clash with Arsenal brought forward 24 hours.
The Cottagers were keen to give themselves additional time to prepare for Wednesday's Europa League final showdown with Atletico Madrid in Hamburg.
Roy Hodgson's side booked their place in the continental showpiece after a thrilling run which has seen them overcome Shakhtar Donetsk, Juventus and Hamburg.
A statement from the Premier League read: "Given it was the final day of the season, when we always play all our matches at the same time for reasons of integrity, and being mindful of the travel plans supporters will have made, the board felt it wasn't appropriate to move the Arsenal-Fulham match."