Gareth Southgate will be offered a new contract with a significant pay rise to remain England manager beyond 2020.
Southgate has two years remaining on his current deal but the FA want to reward his success in leading England to the semi-finals of the 2018 World Cup.
The performance in Russia is likely to see Southgate attracting interest for club jobs when they become available next season, and the FA believes it makes sense to offer him a new contract now.
Talks will begin next week when Southgate returns from his holiday. Any new deal is likely to take him through to the 2022 World Cup in Qatar.
FA chief executive Martin Glenn says England have unfinished business under Southgate and they want to become one of the top four countries in the world.
Speaking on Wednesday, Glenn said: "Gareth has been excellent - we'd like him to stay beyond 2020. I think we'd both like that.
"Benchmarks are always the question and we can never compete with the Premier League in terms of pay - everyone knows that.
"Gareth is on a journey. He loved the World Cup and he's built his own belief that we can go further and that motivates him and (assistant manager) Steve Holland. One of the most powerful things he said after our defeat to Croatia was we haven't done the job."
He has been shortlisted for The Best FIFA Men's Coach of 2018 alongside the likes of Manchester City's Pep Guardiola and Liverpool 's Jurgen Klopp.
Southgate was initially appointed interim manager when Sam Allardyce's 67-day reign as England boss came to an end, but was given the job on a four-year deal in November 2016 after two wins and two draws in temporary charge.
The FA has also confirmed it is preparing a bid for England to host the 2030 World Cup.
FA chairman Greg Clarke said "feasibility work" will now be carried out but no final decision will be made until 2019.
One option is for a joint bid with the other home nations, while the UK government has said it will support a joint bid led by England.