The 34-year-old Beckham was photographed on Sunday using an inhaler during LA Galaxy's 5-4 defeat on penalties by Real Salt Lake in Major League Soccer's championship game in Seattle.
"David has suffered with this since he was a young boy, but it has obviously had no effect on his performance," Beckham's agent Simon Oliveira was quoted as saying in the Daily Mail.
"He has never sought to make it public but if it does inspire any sufferer to think they can achieve great things like many other sportsmen have done then so much the better."
Beckham played extra time with Galaxy for the second time in two weeks on Sunday and was coughing badly after the game having struggled with a cold in the build-up to the MLS final.
He had pain-killing injections before the match to cope with a bruised right ankle and limped through extra-time with Galaxy having used all three substitutes.
Beckham scored his penalty but Galaxy captain Landon Donovan was among those to miss and Salt Lake won the shootout after a 1-1 draw following extra time to claim a surprise triumph.
He will rejoin AC Milan on loan in January as he bids to make England's World Cup squad for next year's finals in South Africa.
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