Athletic will compete in the Europa League after winning the Copa del Rey last term.
"We're coming off the back of a great season and that always makes you start again with optimism," Valverde said at his first press conference of 2024/25 .
"We're playing in Europe again for the first time in a while, but we want to test ourselves and see how we can handle four competitions. It's a challenge and it will be tough, but exciting at the same time."
Valverde was also happy for their Euros winners Unai Simón, Dani Vivian and Nico Williams, who will be back with the team in four weeks time (August 12).
Valverde said: "We're happy for them. Happy that they've achieved something as difficult as winning a European Championship. They've shown that by being at Athletic you can be one of the best players in Europe.
"We want to have the best players and for players to want to be here so we can compete at the highest level. We want players who turn out for their national team to do well, because they are good players.
"We have a great group and if we can we want to improve it. We've already seen how ambitious this team is."