The FA have distanced themselves from Arsene Wenger becoming the next England manager after confirming their preference is for an Englishman.
Football Association chairman Greg Clarke, while answering questions from MPs on alleged corruption in football, said the governing body "would like an English manager if we can get one".
He said: "But if we can't, we'd like someone who has managed extensively in the Premier League so he understands the English football system, its development, the EPPP (Elite Player Performance Plan) etc.
"And I think we'd be crazy to appoint anyone who has never worked in English football. So it's a taxonomy."
Arsenal boss Wenger recently stated he was open to managing England "one day" but backed interim boss Gareth Southgate to take on the job full-time.
Southgate fits the criteria having managed Middlesbrough in the Premier League for three years between 2006 and 2009, when they were relegated.
Current Englishmen managing in the Premier League are Eddie Howe, Alan Pardew, Sean Dyce and Mike Phelan.
Steve Bruce, who recently took over at Aston Villa, was interviewed before the job was given to Sam Allardyce in the summer and is one of just five English managers outside the top flight that have Premier League experience.
Leeds United boss Garry Monk is another, as well as Neil Warnock, Steve McClaren, who failed to take England to Euro 2008 as boss, and Southend manager Phil Brown.
Facing a grilling from the Commons Culture, Media and Sport select committee on Monday, FA chairman Clarke defended their handling of Allardyce's departure after he was filmed by a newspaper discussing how to "get around" FA transfer rules.
Clarke said Allardyce "gave 100 per cent to FA commitments as manager" and "significant enquiries" on the ex-West Ham boss "raised no significant issues" before his appointment.
Clarke confirmed a financial settlement was made with Allardyce to terminate his contract by mutual consent, but he did not disclose the amount because of a confidentiality agreement.
Asked to justify the pay-off in light of grassroots issues, including a lack of funding, Clarke said: "I obeyed the law of the land and took the advice of a QC. Any right thinking person would rather spend money on facilities. But we will always obey the law. We took external advice."