The Paraguayan striker helped the Lisbon giants to league victory last season, and has been linked with the Hammers for some time.
Sam Allardyce is a big fan of the South American, seeing him as a good option as he looks to bring a more attractive rand of football to east London.
The 31-year-old has been one of the continent’s most prolific front-man for quite a while, with his record since arriving in Portugal in 2007 better than a goal every other game.
West Ham are understood to be willing to pay close to £10m for his services, yet the player himself has reservations surrounding a switch to the Irons.
The Hammers are unlikely to give up just yet, and could attempt to persuade the goal-getter to make the move to English football.
An alternative option Is Ecuadorian World Cup star Enner Valencia, who is valued at around £12m by Pachuca.