No side has ever come back from a three-goal first-leg deficit in the Europa League but that is the task that faces Juan Antonio Pizzi's men this week after a disastrous showing in Switzerland.
Matias Delgado's brace and a late Valentin Stocker goal would have had St Jakob-Park in raucous mood last week, had it not been played behind closed doors due to crowd trouble in a previous tie.
It did, however, lay the foundations for Basel's likely progression, with the record books pointing to an exit for Valencia - UEFA Cup winners under Rafael Benitez in 2004.
Basel coach Murat Yakin captained the club on their last visit to the Mestalla when the Swiss side were routed by one of the best Valencia teams in recent years.
John Carew, playing alongside the likes of Santiago Canizares, Roberto Ayala and Pablo Aimar, struck a brace in a 6-2 victory and the class of 2014 require a similarly dominant showing to move into the final four of this year's competition.
As well their Europa League campaign looking likely to come to an end this week, Pizzi's Valencia have also lost ground on the top six in La Liga.
Without a win in their last four matches in all competitions, Valencia's hopes of qualifying for Europe next season look all but over, although they will take heart from their strong home form this term.
Pizzi has only tasted defeat once at home during his tenure, which began late last year, but Basel have conceded only one goal in five Europa League fixtures this term.
After their defeat in Basel, Pizzi - whose side were 3-0 first-leg winners over Ludogorets in the previous round - said he was "ashamed" at how his charges performed in the first half, but added: "I didn't think the game with Ludogorets was over and I don’t think this one is, but it will be difficult.
"We will do everything possible to get through in this tie."
After Sunday's goalless draw with Real Valladolid, he reaffirmed his belief that Valencia are in with a shout of progression, saying: "The last thing we lose is hope."
Basel's Stocker (adductor) and Philipp Degen (calf) are ruled out of the trip, while Marek Suchy is suspended.
Pizzi has injury concerns too, having called up a host of youth players to deal with the absences of squad members such as Diego Alves, Philippe Senderos and Victor Ruiz.
Captain Ricardo Costa has returned to training following an ankle knock but Thursday's game could come too soon for him.
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