Bilbao will host Torino in the second leg of their UEFA Europa League last-32 tie on Thursday before taking on Eibar in La Liga on Sunday and Espanyol in a Copa del Rey semi-final second leg next Wednesday.
Eibar lie 11th in La Liga, one position ahead of Bilbao on goal difference, with both clubs joined by 10th-placed Real Sociedad on 27 points.
If Valverde's men defeat Eibar, who have lost five consecutive games, they could rise as high as ninth depending on other league results and be within three positions of Europa League qualification for next season.
But Valverde will not prioritise La Liga over Bilbao's two shots at cup glory this term, while he insists playing three critical matches in the space of a week may help his side rather than hinder them.
"It is one of the most crucial moments of the year. We will look to progress to the last 16 with victory against Torino and on Sunday we play against a team level with us in the league before facing the cup semi-final," the 51-year-old coach said.
"Although the matches are all close, when you win the momentum carries you and you don't feel fatigued. The aim is to go into these seven days looking to do equally well in all three competitions."
Bilbao drew 2-2 at Torino in the round of 32 first leg last week.
Inaki Williams gave the Spanish visitors a ninth-minute advantage before a brace from Maxi Lopez saw Torino lead 2-1 at half-time.
Bilbao needed a 73rd-minute equaliser from Carlos Gurpegi to leave Italy with a draw, and Valverde hopes the home crowd at San Mames will inspire his players to overall victory.
"Hopefully the crowd will motivate us a lot," he said.
"We have the advantage of San Mames, it should be full."
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