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 followed 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.
“The last Olympic Games the four associations had to play under the Great Britain denomination," Blatter told reporters at the CONMEBOL Congress in Paraguay on Wednesday.
"I spoke with the four presidents in Belfast and they are going to seek the same solution for the 2016 Games because they want to participate in soccer and if they want to take part they must abandon the national identification of the four associations (for the Olympics)."
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 jeopardise 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.
(Reporting by Justin Palmer; editing by Ken Ferris and Martyn Herman)
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