Sources have reportedly told the website the Hammers are ready to drop their pursuit of the AC Milan striker and move on to other targets.
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Barcelona have made a concerted effort this summer to add further depth to their attacking line to attempt to take some of the burden off Luis Suarez, Neymar and Lionel Messi.
But the 29-year-old has kept West Ham waiting as he pushes for a move to Ligue 1 champions Paris Saint-Germain, managed by his former Sevilla boss Unai Emery.
Carlos Bacca scored 18 Serie A goals in his first season at AC Milan last term.
‘Bacca is a player of an worldwide standard, ‘ said AC Milan boss Vincenzo Montella.
Bacca was offered £3.7m a year to play at the Olympic Stadium but he is holding out for a chance with a top European club.
The Hammers have been in talks with Bacca for several weeks as they look to bring in a new striker, but the Colombia global has been stalling on whether he wanted to move to the Premier League.
He would command a fee of around 30 million euros, wherever he goes.
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For Milan, losing Bacca would be a major blow, with a prospective takeover by a Chinese consortium and subsequent investment seemingly the one thing that could keep him in Italy.
