The Football Association will seek to cut the number of foreign players permitted in Premier League squads, even if the United Kingdom does not leave the European Union.

The FA has drawn up proposals to deal with Brexit under which the allowance of non-homegrown players in the 25-man squads would be reduced from 17 to 13, and will pursue that course regardless.

The government asked the FA, Premier League and Football League to agree a joint policy on the approach to players arriving from overseas post-Brexit and has indicated it would adopt the governing body’s proposal once any split from the EU is complete.

The FA’s chief executive, Martin Glenn, has presented the plans to top-flight clubs although they appeared to fall at the first hurdle when rejected by Premier League chairmen at their meeting last week. However, the FA, which runs the current system with Home Office approval, believes it is in a position of power and its stance is not expected to shift.

Talks are ongoing with the clubs, who are anxious to avoid a “no deal” scenario in which EU players would have to fulfil the same criteria as non-EU footballers to gain work permits. If those rules were in place, 65% of the Premier League’s current European players would not have met the “governing body endorsement” (GBE) threshold to be able to represent an English club.

Five clubs, including Manchester City and Tottenham Hotspur, have the maximum 17 overseas players, while four more teams, including Chelsea and Liverpool, have 16.

The FA has argued that the proposals would not prompt a net fall in the number of imported players, given there are about 260 overseas players in the Premier League, equating to an average of 13 per club. It argued that if sides had been limited to playing their most-used 13 non-homegrown players last season, only 42 of 10,469 appearances would have been impacted.

The governing body has tried to convince the clubs to sign up by offering to relax GBE criteria and create a fully open market. That would allow Premier League clubs to secure elite talent from South America, Africa and Asia as easily as they currently access European players.

It believes this would focus minds on purchasing talent ready for the first team and maintain the league’s global popularity, while also potentially boosting the number of English players in line for first-team football. Only 62 of 220 starters in the top flight were eligible for Gareth Southgate’s England side this month, with that figure generally hovering around the 30% mark.

Any plans would not come into force before 2021, unless the government drops Brexit plans, and would probably be followed by a review of the loan system to prevent the stockpiling of players. But the FA, regardless of the outcome of the government’s negotiations with the EU, is committed to increasing the homegrown quota to boost the proportion of English players in the elite division. It is comfortable with the Football League’s arrangements, where seven of a club’s 18-man match-day squad must be homegrown, including at least one who has been developed in the team’s youth system.

A homegrown player in Premier League terms is one registered with a club affiliated to the FA or Welsh FA for three seasons or 36 months before his 21st birthday.