Dyke, the Football Association chairman, has proposed raising the number of English players in club squads from the current eight to 12 in a move to be phased over four years from 2016.
Former England and club managers have supported the proposals, designed to improve the national team’s performance, but Fox said that was not the case at boardroom level.
“I am not supportive of it (the quota proposal) and, to be frank, I don’t think I’ve spoken to a counterpart within the Premier League that is supportive of it,” he told a Sport Industry Breakfast Club meeting.
“I don’t think that system leads to the desired outcome, in fact I think it probably leads to the exact opposite outcome,” added the American.
“What could happen is some of our best players at 13, 14, 15, 16 get poached because it’s much easier to take them at that age than to buy them as a fully formed star, decimating the academy system and making really my academy system not financially viable.”
Fox also questioned the reasoning behind the proposal.
Dyke set up the England Commission in 2013 to look at ways of improving the chances of young English talent to succeed at the highest levels.
The Commission identified a lack of quality coaching and opportunities for home-grown players to play competitive first team football between the ages of 18 and 21.
“I still look at it and wonder what the issue is. I watched the (2014) World Cup as everybody did,” said Fox.
“There were 11 starting Premier League players on the pitch for England and the bench was filled with starting Premier League players.
“There’s something else that’s not right if the United States, which had one current Premier League player in Jozy Altidore and Clint Dempsey who has left the league, makes it past the group stages and England doesn’t.”
Fox, whose club has provided a stream of England internationals, suggested playing regularly against the world’s top talent in the Premier League was “far more important for development than creating some artificial quota system.
“I think…there needs to be better coaching and development at a younger age. I don’t think the quota system is a goer,” he added.
(Reporting by Alan Baldwin, editing by Justin Palmer)