Chelsea were linked with the Paraguayan international earlier this month, but now look to have settled on a move for Samuel Eto'o instead. None of Chelsea's three senior strikers have scored in the club's three matches so far.
That left West Ham in pole position, but they now face intense competition for his signature from the La Liga giants.
The 30-year-old Benfica forward is valued at around £13m by his Portuguese club, and Barca boss Martino is thought to be willing to sanction a move after David Villa was allowed to join Atletico Madrid earlier this summer.
The new Nou Camp manager wants another attacking option following the departure of the Spain international, and Cardozo reportedly fits the bill.
Lionel Messi is the club's only option through the middle, with Cesc Fabregas occasionally used in a false nine role.
So Martino wants the extra security of another forward to call on should injury strike.
Reports in Spain claim he's looking to add one more striker to his squad before the deadline.
And with Chelsea now looking elsewhere, the Spanish giants don't have much competition for Cardozo. West Ham boss Sam Allardyce is on the lookout for another forward, but the Hammers can't offer the South American hit-man Champions League football.
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