The proposal, to be put to the clubs this week, would mean significant changes to a number of sides. Thirteen clubs have more than 12 overseas players in their first team squads this season.
The FA would in return agree to give a governing body endorsement, usually issued for a non-EU/European Economic Area elite player to help the development of football in England, for a work permit for every foreign player who gets a contract with a Premier League club, the report said.
If the clubs fail to reach agreement with the FA on Brexit, they could face a "no-deal" scenario where all EU players would have to fulfil the same criteria that non-EU players do now to get a work permit, the report added.
"We are continuing to work with the Premier League, EFL (English Football League) and a range of government departments, including: DCMS (Department for Digital, Culture, Media and Sport); Home Office; Treasury during this consultation period," an FA spokesperson told Reuters.
British Prime Minister Theresa May said on Monday that there were still considerable unresolved issues with the European Union over Brexit as the two sides approached the "endgame" in negotiations for departure from the bloc. (Reporting by Shubham Kalia in Bengaluru; Editing by Ian Ransom and Christian Radnedge)
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