A deal for the USA international fell through in the final days of the winter market.
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However, the Cottagers remain keen and are back in contact about setting up a move this summer.
PSV were happy to sell Pepi last week as Fulham put €35m cash on the table for the attacker.
However, left with no time to find an adequate replacement, PSV were forced to pull the plug on the deal.
The Dutch giants remain open to doing business with Fulham and talks are now back on over the future of Pepi.