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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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.