Bilbao's San Mames stadium is due to host three group games and a round-of-16 tie in June in the European Championship but has been unable to guarantee to UEFA that fans will be allowed to attend games.
European football's governing body has given the Basque city, along with Munich and Dublin, until Monday to provide assurances that some spectators will be allowed into their stadiums.
"For us as a national team and as a country we feel it is fundamental to remain as a host nation," Rubiales said.
"It's true that there's some difficulties in Bilbao but UEFA need to decide on that. For us, if they decide to remove it, it would be terrible for us if those games went to another country.
"I'm going to do everything that's in our powers in order for Spain to remain as a host nation and La Cartuja is a fantastic stadium that has everything it needs to host it.
"We have a relationship with the regional government and the stadium and so if this were to happen Seville would be our first choice, but it's not up to us.
"Hosting three national team games and a last-16 tie would be a big deal for us, both in terms of for fans and economically."
