Sunday's game at the Mestalla sees Valverde return to Valencia, where he spent eight months in charge last season, narrowly missing out on qualifying for the Champions League.
The team have declined since Valverde swapped Valencia for Bilbao in the summer, with Los Che sacking his initial successor Miroslav Djukic in December. Athletic, meanwhile, have gone from strength to strength under Valverde and are in the driving seat to qualify for Europe's elite competition.
However, the arrival of Juan Antonio Pizzi has provoked a mini-revival at Valencia, who had put together an unbeaten run of six games before they suffered a 1-0 defeat at Rayo Vallecano last Sunday.
Valverde told a press conference: "I consider Valencia to be a direct rival because of their potential and because in the last couple of months they've been playing well and rising up the table.
"They are very strong on the wings and are always trying to get into your area. They have players that can put their chances away and a strong midfield too with players like [Dani] Parejo, [Seydou] Keita and [Javi] Fuego. If they dominate you they can make you suffer because they have decisive players."
Sunday's game comes a week before Athletic visit Villarreal, their closest rivals in the race for the fourth Champions League spot.
"Both are big teams and both are big games. I don't know if they will be decisive, but they will certainly be important," said Valverde on a crucial eight days for his club.
Valverde is still without injured forwards Ibai Gomez and Kike Sola but can count on an in-form Aritz Aduriz, who hit a hat-trick in last week's resounding 4-0 win over Granada.
Valencia meanwhile are weakened due to the loss of captain Ricardo Costa, who is carrying an ankle injury, and full-back Antonio Barragan, suspended for getting sent off for two bookings at Rayo.
Pizzi insisted his team have learnt from the mistakes the made in Vallecas, telling reporters: "We didn't do certain things as we should have done and we've talked about it all week. We all agree that there are things we need to change."
The loss to Rayo means Valencia need to recover 15 points on Athletic if they want to get into the Champions League, but Pizzi insisted his team would not lose focus even though their main objective appears so distant.
"We don't need to think about the Champions League to make this game important," he said.
"Whether we qualify for the tournament or not, we will play every game as if it were our last chance."