The 24-year-old is one of the mostly highly sought after players this summer, attracting interest from a host of top flight sides.
Pepe has been strongly linked with a move to Anfield, with Lille confirming the Reds had made enquiries, which was later denied by the Merseysiders.
But Everton are now reportedly considering making a move for Pepe, according to the Telegraph .
Lille have slapped a £58.5 million price tag on their star man however, and it is not known whether the Toffees are prepared to fork out that sum on one player.
Everton have been big spenders in recent transfer windows, paying large fees for the likes of Richarlison, Cenk Tosun and Gylfi Sigurdsson.
Now boss Marco Silva wants to add a left-footed attacker to his ranks, and Pepe is just one player he has been keeping tabs on.
Ajax’s David Neres is also in the frame, with his asking price likely to be significantly lower than Pepe’s at around £35 million.
Barcelona’s Malcom and Lyon’s Bertrand Traore are also on the list of targets, with the former already having been told he is surplus to requirements at the Nou Camp.
It is thought Silva would prefer a move for Malcom, given his asking price is said to be around £31 million.
He also wants to add Chelsea’s Kurt Zouma to his squad after having him on loan last season, but it is as yet unknown as to to whether Blues boss Frank Lampard will allow the central defender to leave the club.
Everton will not be making a move for ex-Chelsea striker Diego Costa though.
The Atletico Madrid frontman has been linked with a switch to Goodison Park after he told he could leave the Spanish club, but Silva has no interest in the 30-year-old.