The RFEF is led by Juan Luis Larrea on an interim basis after former president Angel Maria Villar was forced to step down on corruption charges.
"We can confirm that FIFA recently sent a letter to the RFEF showing its concern with the situation the federation is in and reminding it that... all member associations should manage their affairs independently," FIFA said in a statement on Friday.
"All associations must be assured that there is no outside interference from third parties in its internal affairs. FIFA is in contact with the RFEF and in the next few weeks a delegation of FIFA and UEFA members will travel to Madrid to analyse the situation the RFEF is in."
Spanish newspaper El Pais reported that FIFA's concerns centre around the government's sports department pushing to hold new federation elections.
A statement from the RFEF said its president Larrea had discussed the situation with FIFA members at the World Cup draw on Dec. 1.
"The RFEF passed on these (FIFA's) concerns to the minister for sport and is expecting to organise a meeting on the matter. The RFEF wants everything to return to normal, that has always been the main objective of the current board of directors.
"We underline that we all want the national team to participate in the 2018 World Cup, especially after its brilliant qualifying campaign."
Spain captain and Real Madrid defender Sergio Ramos, speaking ahead of the Club World Cup final in Abu Dhabi, added: "I cannot believe that Spain could lose what we have worked so hard for on the pitch due to an institutional dispute, I struggle to believe that."
Spain's prime minister Mariano Rajoy said he was not concerned by the suggestion his country would be barred from competing in the World Cup.
Spain won the World Cup for the first time in 2010 and are one of the favourites to lift the trophy in Russia next year.
"I cannot contemplate that scenario, I'm absolutely convinced Spain will go to the World Cup and that we are going to win it," Rajoy told reporters in Brussels after a meeting of European Union member states.
"The government's behaviour is exemplary and those in charge of the department for sport (CSD) have the total support of the prime minister."
In 2015 Indonesia were banned from competing in qualifiers for next year's World Cup after FIFA said the central government had taken over its federation's affairs. (Reporting by Richard Martin, editing by Pritha Sarkar)
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