Not since 2012 have Los Blancos won the Spanish top flight, but they now require four points from away games with Celta and Malaga in the coming days to overhaul rivals Barcelona and come out on top.
With their European aspirations coming to an end last week, going down 2-1 on aggregate to Manchester United after a brave fight, reality has now sunk in for Celta as they prepare to see out their final two games of the season.
Boss Eduardo Berizzo can hardly be blamed for prioritising the club's rare foray into the latter stages of a continental competition, fielding weakened teams in the league and seeing that reflected in recent results.
Celta have lost five in a row since progressing through to the semi-final stage of the Europa League with victory over Genk, while going further back it is seven losses in eight, the only respite coming exactly a month ago with a comfortable 3-0 win away to a poor Granada side.
During that run the Sky Blues have conceded 17 goals and scored just four, shipping exactly three in each of their last three matches to Athletic Bilbao, Malaga and Alaves, contributing to their slide down the table to their current standing of 13th place.
A top-half finish now out of the question, sitting nine points adrift of Espanyol in 10th with two games left to play, the best Celta can hope for is finishing as high as 11th, but that will likely require them to pull off an improbable double over Madrid and Real Sociedad.
As Barcelona boss Luis Enrique was keen to point out to Real, though, Vigo do have previous when it comes to pulling off big-name scalps this season, becoming the only side to beat both heavyweight teams this term in all competitions.
After beating Barca in a seven-goal thriller here in October, Berizzo's men also got the better of Los Blancos in a Copa del Rey quarter-final double-header, prevailing 4-3 on aggregate to inflict the biggest blow on their opponents' season by denying them the chance of a famous treble.
This match is about far more than revenge for the visitors, however, and they will know that the Galicians are certainly a better team than recent result suggest, with a stronger side expected to be fielded by Berizzo for this huge encounter.
Recent form in La Liga: WLLLLL
Recent form (all competitions): LLLLDL
Had things gone to plan, this rearranged trip to Balaidos would have been the title-clinching evening for Los Blancos. No matter what happens in this midweek tussle, though, the title race will definitely go down to the final day.
For that the neutral has Lionel Messi to thank, with his 93rd-minute strike at the Bernabeu three weeks ago keeping things alive at the top and putting just a little extra pressure on Madrid, who currently trail Barcelona due to their rivals' superior head-to-head record.
That defeat aside, Madrid have held their nerve at the top of the division and have dropped points in just three of their last 14 outings, being held at home by both Las Palmas and Atletico Madrid - the former no doubt feeling like a win due to the late nature of the draw.
That means it is still all to play for with just a handful of days remaining of the campaign, although the formula is far from complicated. A win and a draw for Madrid in their next two matches will make them champions; anything less and Barca, who host Eibar on the final day, will surely be left celebrating a third successive title.
Zinedine Zidane also has the small matter of a Champions League final to look forward to, of course, yet the Frenchman has managed to get his squad rotation spot on, seemingly getting the best out of fringe players - James Rodriguez, Isco, Alvaro Morata and Marco Asensio among them - while at the same time keeping star man Cristiano Ronaldo fully fit.
Finding a way through packed defences has also not been a problem for Madrid, having scored in each of their last 62 competitive matches - including all 36 La Liga games in 2016-17 - which is a record for a side in Europe's five major leagues.
Sixteen goals in their four league outings since going down to Barca also suggests that Zidane's men are not prepared to slip up, with just two games now left to tick off in the league before attention can turn to Cardiff on June 3 and a potential date with destiny.
Whether or not Los Blancos will be competing for a domestic and European double in the Welsh capital will become a little clearer come the end of Wednesday night, but recent form certainly suggests that Zidane's men are in no mood to let history slip through their grasp.
Recent form in La Liga: WLWWWW
Recent form (all competitions): WWWWLW
Zidane has not been afraid to heavily rotate his squad, making nine changes for his side's last away outing at Granada, but with the Champions League taking a backseat for the time being he is expected to name his strongest possible XI on Wednesday.
That means a place up top for Ronaldo, who has scored in nine of his 11 previous meetings with Celta and netted a whopping 18 in all, while Isco could get the nod in Gareth Bale's absence.
Aspas is currently on 18 league goals for the season, just three fewer than Ronaldo, and has found the net in four of his last eight outings.
Berizzo will surely field his strongest available side for the visit of Real, with nothing else now left to play for, so Facundo Roncaglia is in contention to start alongside Gustavo Cabral in the heart of defence
Celta Vigo possible starting lineup:
Alvarez; Mallo, Roncaglia, Cabral, Jonny; Hernandez, Radoja; Aspas, Wass, Sisto; Guidetti
Real Madrid possible starting lineup:
Navas; Danilo, Ramos, Varane, Marcelo; Modric, Casemiro, Kroos; Isco, Benzema, Ronaldo
Head To Head
Celta have lost their last five league meetings with Madrid, all since Berizzo took charge. They have also won just one of the last nine encounters here, with that 2-0 triumph coming in May 2014.
The Sky Blues have lost the other eight matches during that run, although they did pick up a win and a draw in those aforementioned Copa del Rey ties earlier this season.
We say: Celta Vigo 1-3 Real Madrid
Celta have failed to win any of their last eight games in all competitions, crashing out of the Europa League at the semi-final stage and slipping right down the table. They may have picked up victory over Barcelona and Real already this season, but pulling off a similar result on Wednesday against a determined Los Blancos side is surely beyond them on current form.