Nilsson said the Scandinavian country had not yet discussed the possibility of European governing body UEFA breaking away from FIFA but added that nothing could be discounted.
"It's a very special situation and one must be prepared to take special actions," he said in an interview.
"Generally, the Swedish way is not to boycott things. Rather, we believe in influencing things from the inside. (But) it is a very special and extreme situation and we don't close the door for anything."
Despite being rocked by a corruption scandal which saw high-ranking FIFA members arrested in a dawn raid at a Zurich hotel, Blatter was re-elected as president of FIFA at the world governing body's congress last week.
"This is democracy, and in that way one must accept the result, even if one isn't happy," said Nilsson, an affable 58-year-old who was involved in local politics before taking over the Swedish FA in 2012.
"Those who lose have to have respect for the winners, but those who win should also show respect for the large amount, 35 percent, who wanted a different result."
Nilsson said UEFA's future strategy regarding Blatter and FIFA, and any discussions about a possible breakaway, would most likely be discussed when senior officials of Europe's football associations gather in Malta in September.
Whatever the outcome, though, Nilsson is adamant that FIFA needs to change, and that the drop in support for Blatter indicates that more FIFA members are eager to see corruption stamped out.
"We have different cultures in different parts of the world," the former referee said.
"I believe we see these things in different ways, but we have to have respect for openness and transparency and a change of culture in FIFA, which means FIFA can get a very different reputation to the one it has today. That is completely necessary.
"That it (football) would be completely clean from all problems in the future is maybe a little bit naive, but there is great potential for improvement, and that is what we want to see in the first instance."
(Editing by Ian Chadband)
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