La Roja are three-time European champions, triumphing in 1964, 2008 and 2012, while they reached the semi-finals of Euro 2020.
Spain are not considered to be among the favourites for the Euro 2024 crown, with France, England, Portugal and Germany all believed to have a stronger chance of securing the trophy.
However, de la Fuente has claimed that his side's UEFA Nations League success in 2022-23 has left them in good stead ahead of the tournament in Germany, and the 62-year-old is certain that the European heavyweights will be in the fight for the trophy this summer.
Spain will open their Group B campaign against Croatia on June 15 before also tackling Italy and Albania in the group stage of the competition.
De la Fuente backs Spain to challenge for Euro 2024 crown
"We've already faced Italy and Croatia in the Nations League but they are such good national teams; you just need to take a look at their record, their history or their players to realise it," he told UEFA's official website.
"But we can't forget Albania. Albania have really good players, they have developed a lot. I've known them through their Under-19 and U21 teams, and the matches against them were always really tough.
"Their coach is also really good. I rate him highly because he is a very brave and determined coach who has clear ideas. He has contributed a lot to Albanian football.
"The first goal must always be to compete and be in a position to win. I am convinced we will have a chance to fight for the title. However, there can only be one winner and there are many good national teams who can win this trophy.
"I think we are ready and we still have time to keep growing and improving to get that great team we need to be able to fight for the title.
Spain will face Croatia, Italy and Albania in Group B
"It was a very decisive moment [winning the UEFA Nations League] at a very difficult time for us because it was the third or fourth match we were playing together.
"Besides, we had previously lost against Scotland. People around us may have had doubts but the group was convinced about our goals and knew what we wanted to achieve, and the team proved it.
"We have talked about this several times from that first moment and, given that a victory helps you grow, we became stronger - we haven't lost another match since.
"That made the team more confident, but also those new players who just had to follow the current dynamic. Those who were veterans and the captains showed perfect behaviour, and the youngest showed an extraordinary maturity to accept and understand everything they were asked.
"That makes our work much easier. I'm very proud of them. I'm quite thankful because they've made our work much easier. As I tell them, in my opinion they are the best."
De la Fuente confirmed his 26-man squad for the tournament on Friday, with Barcelona's Pau Cubarsi, Atletico Madrid's Marcos Llorente and Girona's Aleix Garcia the three players dropping out.