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The Costa Rica star, who shone at the World Cup, is back at the Emirates after spending three seasons out on loan.

He cut his teeth at Lorient and Real Betis before moving to Olympiakos, where he made a big impact last year.

Campbell, 22, helped the Greek giants to the title and scored in a Champions League last-16 loss to Manchester United.

West Ham have problems up front with £15m man Andy Carroll on the treatment table.

The club-record signing missed most of last season with a foot problem and could be out for another four months.

He requires surgery to fix the issue, leaving the Hammers short of forward options.

Allardyce reportedly sees Campbell as an exciting addition to a side that have been criticised for showing a lack of quality in attack.

But they won't get him easy.

AC Milan are also monitoring the frontman, who has netted 10 goals in 36 games for his country.