The former Manchester United winger confirmed in a press conference on Monday his intention to quit LA Galaxy after the MLS Cup final game on December 1.

And since the announcement, speculation has linked Beckham with a host of clubs from Asia and Europe, but Allardyce is keen to hand Beckham a return to the Premier League with West Ham - but only if his fitness is up to competing to England's top flight.

"Yes, I would like to see a fit David Beckham at West Ham," he told The Sun.

"But he would need to come and do a fitness test like any other player."

Concerns over the 37-year-old's fitness, however, are not shared by the player himself, who believes he has the fitness and desire to still be competitive at the highest level.

"I still feel like I have one more challenge in me as a player, even at 37 years old. I feel that I still can play at a high level. Where that'll be yet, I haven't decided," the former England captain told reporters.

"I have some exciting opportunities on the table."