Casillas made 167 appearances for Spain and captained his country to success at the 2010 World Cup and the European Championships of 2008 and 2012.
The 38-year-old has been at Porto since leaving boyhood club Real Madrid in 2015, but he suffered a heart attack in a training session in May 2019.
Casillas has not featured for the club since and was added to the team's backroom staff in July, yet he was also included in their squad for the ongoing season and has not formally retired.
He did not announce an end to his playing career on Monday, but he thanked Porto president Jorge Nuno Pinto da Costa for allowing him to pursue the RFEF opportunity.
He wrote: "Yes, I will stand for the presidency of the RFEF when the elections are called. Together we will put our federation at the height of the best football in the world: that of Spain.
"I have informed the president of my club, FC Porto, of this decision, to whom I can only express my deepest gratitude.
"We are working with the utmost respect in our candidacy. More than 23,000 voters await us in fair and transparent elections. 139 assembly members will decide.
"Thank you all for all the love I have continually received. Your support and your strength encourage me. Let's go for it! #IkerCasillas2020"
Luis Rubiales has been RFEF president since May 2018, although his tenure got off to a rocky start as Julen Lopetegui was sacked on the eve of the World Cup after agreeing to take the Real Madrid job following the finals.
Spain's coaching difficulties have since continued under Rubiales, with Luis Enrique appointed before stepping away as his daughter, Xana, battled bone cancer. She died in August.
Assistant Robert Moreno stepped up to the senior role but was later replaced by the returning Luis Enrique, with the pair - long-time colleagues and friends - falling out.
Rubiales has insisted the RFEF did not mishandle Luis Enrique's reappointment.
A date for the latest RFEF election, which would appear to see Casillas take on Rubiales, is yet to be confirmed.