Currently, players from outside the EU must gain work permits and pass a series of qualification tests to get a "governing body endorsement" and work permit.
Premier League clubs must have eight "homegrown" players in their squad of 25. These do not have to be British but must have been part of the club for three years before turning 21.
The FA, which has been asked by the British government to come up with a proposal, wants to impose a limit of 13 non-homegrown players in the 25-man Premier League squads after Brexit.
It wants the government to drop work-permit restrictions on non-EU citizens, creating a level playing field regardless of nationality.
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"The proposal would allow the same current access to European players and reduce governing body endorsement requirements for non-European players to the same levels," the FA said.
"In return for this improved access, the FA would like to ensure that the league collectively does not exceed the current number of around 260 non-homegrown players ... This is equivalent to 13 players per (Premier League) club," it added.
The FA believes increasing access, but preventing an increase in current numbers of overseas players, "would benefit all of English football".
It hopes that including more domestic players in first-team squads will help the national side develop talent.
But the Premier League disagrees. It says that it, the Football League -- which represents the 72 clubs in the lower tiers of the English professional game -- and the Scottish Professional Football League all feel "that Brexit should not be used to weaken playing squads in British football, nor to harm clubs’ ability to sign international players".
In a statement on Tuesday it added: "There is no evidence that stronger quotas than exist now would have a positive impact on national teams."
Citing the recent successes of England teams at youth and senior level, the statement said: "We currently operate rules that limit the number of non-homegrown players clubs can have in senior squads, while also working with clubs to operate a world-leading player-development system which delivers for England teams at every level."
CASH GENERATOR
The Premier League also highlighted its global and business success, saying the country benefited from its attractiveness internationally.
"Our competition is watched in 189 countries, 700,000 visitors to the UK per season attend a match, clubs employ 12,000 full-time staff and Premier League football generates 3.3 billion pounds ($4.22 billion) per season in taxes."
The league said it would continue talks with the FA over the matter.
($1 = 0.7824 pounds)
(Reporting by Simon Evans,; Editing by Neville Dalton)
