Last month Bridge said his presence in the squad was potentially "divisive" following newspaper allegations about a relationship between his former partner Vanessa Perroncel and Chelsea defender John Terry.
Beckham, who is in his second loan stint with AC Milan from his Major League Soccer club, was injured in the 87th minute of Milan's 1-0 win over Chievo on Sunday.
England and Manchester United midfielder Michael Carrick says that Beckham's presence within the World Cup party would be welcomed by the squad.
"I think the manager has invited him along in some capacity and however he comes along I'm sure for the lads in the squad it will be good to see him," he said.
BECKHAM'S ENGLAND FACTFILE
Debut: v Moldova (1/9/1996) - won 3-0
Last game: v Belarus (14/10/2009) - won 3-0
"It will give the lads a big boost because he's just got that presence, and great players have that. He's got that all-round presence that people respond to."
Beckham, England's most capped outfield player with 115 appearances, had been bidding to become the first England player to feature in four successive World Cup finals.
Beckham shares the record of playing in three finals with Billy Wright, Bobby Moore, Peter Shilton and Michael Owen.
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