Sevilla, in sixth place, have an outside chance of taking the fourth spot but they must beat Athletic Bilbao and hope both Valencia and Getafe lose their matches in the finale of what has been a gripping race for the league's coveted fourth spot.
Elsewhere in La Liga, champions Barcelona visit Eibar while runners-up Atletico Madrid visit Levante and third-placed Real Madrid host Real Betis.
Unfashionable Getafe have never made it into the Champions League before while Valencia, who were losing finalists in 2000 and 2001, see Europe's top competition as their natural habitat.
Yet returning to the competition seemed like a distant dream when they were languishing 12th in the standings in December and their famously demanding fans were calling for Marcelino's head.
The rebellion began during a 1-1 draw in December with Sevilla when angry fans waved handkerchiefs, the traditional signal of dissatisfaction in Spanish stadiums.
The protests reached boiling point during a game against basement club Huesca later that month and not even a last-gasp winning goal could quell the anger, as fans continued to furiously boo the team and their coach after the final whistle.
After a limp defeat to Alaves in January, reports were rife that Marcelino would be sacked by Valencia, but he was helped by public support from his players and clung on to his job.
In the space of four months, Marcelino has gone from persona non grata to being on the verge of becoming Valencia's first coach to secure successive top-four finishes since Unai Emery in 2012.
A 12-game unbeaten run of six wins and six draws helped stave off further rebellions from supporters or the club hierarchy and they sneaked into fourth last week with victory over Alaves as Getafe fell to a 2-0 defeat to Barcelona.
"There has been a lot of tension, a lot of work and a lot of effort to get here, I don't think Valencia have had a season like this for a very long time," Marcelino said.
"I just hope we don't pass up this opportunity and get the job done. We aren't there yet but we're in the best possible position."
(Reporting by Richard Martin; Editing by Toby Davis)
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