The 63-year-old has had huge success since being appointed Spain manager in December 2022, guiding the team to the 2023-24 UEFA Nations League title and European Championship crown in 2024.
Under De la Fuente, Spain have won 18 of their 23 matches in all competitions, losing just twice, and they were 4-1 winners over Switzerland in their last game in the Nations League on September 8.
La Roja are currently preparing to take on Denmark and Serbia in the same competition, but there is some doubt surrounding the long-term future of De la Fuente due to his contract situation.
As it stands, the manager's deal is due to expire after the 2026 World Cup, and he is said to be on the same wages that he was collecting when he transitioned from the Under-21s.
De la Fuente unhappy with Spain contract situation
"It's not normal for a European champion to be left without a contract. I don't know if the same would happen with Luis Enrique... this is not normal. I've had offers; that's expected," he told Cadena SER.
"But it's abnormal for the reigning European champion to be left without a contract. I have the same terms as when I transitioned from the U-21s... it would only be fair to sign a new contract now."
Spain will be aiming to make it successive wins in the Nations League when they tackle Denmark on Saturday night, before welcoming Serbia three days later, but they are without some key players for the next two games.
Williams becomes latest Spain withdrawal
Nico Williams, who was one of Spain's star players at Euro 2024, has been forced to pull out of the squad due to a muscular problem, with Sergio Gomez called up as his replacement.
Ferran Torres and Bryan Gil have also been forced to pull out due to injuries, while Unai Simon, Dani Carvajal, Robin Le Normand, Rodri, Dani Olmo and Gavi are among those unavailable for selection.
Oscar Mingueza has been among those to benefit in the latest squad, with the 25-year-old hoping to be given the chance to earn just his second cap for the national side in the October internationals.
Meanwhile, Bryan Zaragoza has also been included, with the 23-year-old, who is on loan at Osasuna from Bayern Munich, in strong form in the early stages of the 2024-25 campaign.