"We can confirm that FIFA has received a letter from the Costa Rica FA regarding last Friday's World Cup qualifier," said football's governing body in a statement.
"FIFA will now analyse the content of the letter and next steps will be determined in due course."
Furious Costa Rica coach Jorge Luis Pinto said the match was an "embarrassment to football" after his side lost 1-0 in Denver on a snowy field with a covering that became deeper as the game wore on.
It said the conditions were a threat to "the physical integrity" of the players and said stadium officials had come on to the pitch to clear the snow while the ball was in play.
Furthermore, the pitch markings "disappeared" and the "the movement of the ball became impossible due to the quantity of snow on the pitch."
Fedefutbol also demanded sanctions for "all the officials who were involved in the decision to keep playing this game."
"The complete opposite happened in Europe where the snow forced the match between Northern Ireland and Russia in Belfast to be postponed," it added in a separate statement.
"We don't want to create false expectations but we are fighting for rights which we think we violated during this match," said Fedefutbol treasurer Rodolfo Villalobos.
