Beckham is to leave LA Galaxy next month and West Ham could be one of a number of teams interested in the East Londoner as he embarks on his last major challenge.
“Yes, I would like to see a fit David Beckham at West Ham. But he would need to come and do a fitness test like any other player,” Allardyce told The Sun.
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
Who of Europe’s top strikers will move to England this summer?