England manager Fabio Capello has spoken to Beckham and admits 'it looks like he is out of the World Cup.'
But although Beckham will turn 35 in May, former Manchester United team-mate Cole does not think the midfielder - currently on loan at AC Milan from Los Angeles Galaxy - will want to retire on such a low note.
Agony: Beckham was in obvious distress after picking up his injury on Sunday
'He'll come back from the injury, I don't think he'll want to retire on this note,' Cole told BBC Radio Five Live.
'He'll work his socks off to try to get himself fit. It's devastating news for David, his heart was set on going to a fourth World Cup. He will be heartbroken.
'It's not a nice injury, there's a lot of pain and it's a long way back.'
Beckham had looked certain to be part of Capello's 23-man squad for this summer's finals in South Africa, despite being largely limited to substitute appearances.
Old pals: Cole has backed his former England and Manchester United team-mate to bounce back from his latest disappointment
'Every time he's come on for England, everyone knows his quality,' Cole added. 'He came on for 20 minutes at Old Trafford last week and he was fantastic.
'If he had gone to the World Cup, I think he will be missed, even if as an impact player.'
Capello will be dreading any further injuries in the coming months, particularly to the likes of Wayne Rooney, but Cole added: 'Injuries are part and parcel of football, we can't wrap our players in cotton wool.
'You just hope they get through the season unscathed and do well in the World Cup.'
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