Valverde, who took over at Valencia in December on a short-term deal until the end of the season, has refused to answer any questions this week regarding his tenure in charge beyond the trip to Sevilla.
With Valencia going into the game knowing a win at the Estadio Ramon Sanchez-Pizjuan will guarantee them fourth place in La Liga and a spot in next season's Champions League, Valverde has kept talk of his position off the table.
"I prefer to focus on this match, and I will speak about my future after," said Valverde.
Valencia are in a straight head-to-head battle with Real Sociedad for fourth, with Valverde's side holding a two-point advantage over their rivals who head to La Coruna to face a Deportivo outfit fighting to avoid relegation.
Los Che are on a run of four successive victories without conceding a goal to give themselves another shot of playing club football at Europe's top table.
"Now that we have the Champions League spot within reach, missing out would be a disappointment for us, despite how the season has gone," added Valverde.
"We have one final important game against a team strong at home, and we are focused, while Real Sociedad plays against a team that also has everything to play.
"We have to start our game on the premise Real will win theirs."
Sevilla can finish no better than their current position of ninth, but that may yet be enough to assure them of a place in the Europa League.
With Atletico Madrid finishing third and winning the Copa del Rey, it means whoever finishes seventh - almost certainly Real Betis - will be in Europe.
Sixth-placed Malaga, who are guaranteed to finish in the top seven, are currently banned from European competition next season due to financial irregularities, although they have appealed to the Court of Arbitration for Sport, with a verdict due on June 4.
If that appeal is upheld, eighth-placed Rayo Vallecano then come into contention, but they have been denied a licence for European football next season by the Spanish Football Federation on financial grounds.
An appeal was rejected, but they will also approach CAS should Malaga fail with their bid to have their ban overturned.
Should Rayo also be denied, ninth then becomes a Europa League spot, with Sevilla needing to beat Valencia to retain that position.
Coach Unai Emery, who formerly managed Valencia, said: "We have not met expectations this season. No one is satisfied.
"But within that disappointment ninth is the best we can do, so we must fight tooth and nail for it.
"If it is a way to Europe, to not fight would be foolish."