Carlo Ancelotti's men will enter the match hoping to avoid a third defeat in less than a week, with Sunday's home El Clasico loss to Barcelona followed by a 2-1 reverse at Sevilla on Wednesday.
Those results have seen Real drop to third in the table, two points behind Barcelona, and three adrift of city rivals Atletico.
It means Saturday's fixture in the Spanish capital takes on extra significance, with Real's title chances hinging on a positive result.
Defender Pepe and midfielder Xabi Alonso remain convinced they can still usurp their rivals and win the league, though, and they will take comfort from the fact that Barca and Atletico will meet on the last weekend of the season.
"There are still matches left and it's still possible. We have to be ready to win Saturday's match against Rayo," Pepe said.
"Now we have no room for error. We have to fight knowing who is in the battle for the Liga, and knowing that there is no room for mistakes."
Alonso, who gave the ball away in the build-up to one of Sevilla's goals, added: "There is still time to win.
"Atletico and Barcelona are there, who have to make a mistake, and we cannot falter, but we have to believe."
Gareth Bale arrived in Madrid to much fanfare in the close-season, reportedly becoming the world's most expensive player.
And now would be the opportune moment to show why Real spent so much time – and money – in chasing him, with the Wales international going more than a month without a goal for his club.
One man who is having no problems finding the net is Cristiano Ronaldo, who tops the league's scoring charts with 27.
At the other end of the field, Real will welcome Sergio Ramos back from suspension.
Rayo Vallecano travel to Santiago Bernabeu in a buoyant mood, having embarked on a five-match unbeaten run that has included four wins.
That form has helped them move five points clear of the relegation zone but they left it late on Wednesday, beating Osasuna 1-0 thanks to Joaquin Larrivey's penalty in second-half stoppage time.
They gave Real a run for their money in November's reverse fixture, when a pair of Jonathan Viera penalties in the second half set up a nervy finish.
Rayo do have the propensity to get beaten badly, though, having conceded four or more goals in eight league fixtures this season.
And for that reason alone, they will be wary of a Real side desperate to atone for a poor week.
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