At London 2012 Britain fielded a unified soccer team managed by the FA, after a 52-year absence, although at the time it was seen as a one-off move to mark the home Games.
The British Olympic Association (BOA) said on Tuesday that the FA had confirmed its desire to send a team to Brazil.
"We have received confirmation from the FA of their intention to enter into the qualification process for Rio 2016 for both men and women's tournaments," a BOA spokesman said.
The qualification process for men's is this year's Under-21 European Championship with the four semi-finalists sealing a place in the Olympic tournament.
The top three European sides at the women's World Cup will also enter the Olympics.
World soccer's governing body FIFA would still have to sanction a British team.
Debate has raged over a British team, with the Welsh, Scottish and Northern Irish FAs concerned that agreeing to unite for the Olympics would jeapordise their independent status within FIFA.
Several Welsh and Scottish players played at London 2012 without the blessing of their FAs.
Britain's men, captained by former Manchester United forward Ryan Giggs, and women both lost in the quarter-finals.