If more clubs fell into the hands of overseas owners, the system, the bedrock of English league football since it began in the 1880s, could change, Bevan told the annual conference of the Professional Players Federation.
"There are a number of overseas-owned clubs already talking about bringing about the avoidance of promotion and relegation in the Premier League," he told delegates, without specifying who they were.
"If we have four or five more new owners, that could happen," he said, adding that he hoped any such move could be avoided.
Ten of the 20 Premier League clubs are owned by foreigners, including champions Manchester United, league leaders Manchester City and 2010 League and FA Cup double winners Chelsea.
For any change to be made to the structure or laws of the Premier League, 14 of the 20 need to vote in favour.
There is no relegation and promotion in the major U.S. sports of American Football, ice hockey, baseball and basketball, so the concept is not one that the American owners of United and Liverpool, Aston Villa or Sunderland grew up with.
Last week Liverpool's managing director Ian Ayre was widely criticised for suggesting that Liverpool, owned by American John W. Henry's New England Sports Ventures, could raise more overseas television revenue if it broke away from the collective marketing stance of the Premier League.
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