The Colombian striker has been linked to Arsenal and Chelsea this month.
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Villa rejected two bids from West Ham, with the second just short of Al-Nassr's offer.
According to L'Equipe, Duran is close to joining Cristiano Ronaldo's side, having agreed personal terms.
PSG were also interested, but Al-Nassr's financial package is superior.
Despite starting only four Premier League games this season, Duran has scored 12 times in 28 appearances.