The British Olympic Association (BOA) said on Tuesday the English FA had confirmed its desire to send a team to Brazil.
"We have been consistently clear in our opposition to Team GB," a Scottish FA spokesperson was quoted as saying by the BBC.
Scotland's stance follows that of Wales who expressed their disquiet on Tuesday.
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.
Debate has raged over a British soccer team, with the Welsh, Scottish and Northern Irish FAs concerned that agreeing to unite for the Olympics would jeapordise their independent status within soccer's world governing body FIFA.
Several Welsh and Scottish players played at London 2012 without the blessing of their FAs.