A worst case scenario could see them denied a place in the Europa League semi-finals by AZ Alkmaar, and shoved out of third place and La Liga's last Champions League automatic qualification slot.
Valencia trail AZ Alkmaar 2-1 ahead of Thursday's second leg at the Mestalla, where fans have whistled them off in their last few home games, while their flagging league form has seen them notch only three wins in their last 14 outings.
A surprise victory at the Bernabeu, however, could boost the standing of one of La Liga's longest serving coaches, who is not expected to renew his contract at the end of the campaign should he survive until then.
"I am used to the speculation over my future," Emery said on Wednesday. "I continue with my work and take no notice of it, and I don't see the players affected by it either."
Real, who booked their place in the Champions League semi-finals on Wednesday, are closing on their first title in four years and maintain a six-point lead over chasing Barcelona with eight matches left to play.
Jose Mourinho's men have 78 points from 30 matches and with 100 goals scored to date have the league record of 107 set by John Toshack's Real side in 1990 well within their reach.
Valencia are 30 points back in third, just one ahead of fourth-placed
Cash-strapped Zaragoza's spirited attempt at a great escape has seen them climb off the bottom taking 13 of the last 18 points available, and have claimed the scalps of Villarreal, Valencia and Atletico Madrid along the way.
After last weekend's 2-1 win over Sporting Gijon, coach Manuel Jimenez said they were "out of intensive care", but they remain four points from safety.
The champions, however, have won their last eight league games and booked their place in a fifth-consecutive Champions League semi-final beating AC Milan on Tuesday.
Pep Guardiola will probably have to shuffle his defence again as Gerard Pique is a doubt with a muscle strain picked up against Milan, and Eric Abidal out for the rest of the season.
There are also high-profile clashes in the battle for the two remaining Champions League slots and the Europa League places, with only six points separating third-placed Valencia, on 48, from eighth-placed Sevilla.