The Catalan minnows, in the top flight for only the fourth season in their history, are second and trail Los Blancos by two points.
After Girona's goalless draw with Real Sociedad last weekend, Madrid had the chance to put distance between themselves and Michel Sanchez's side, but they also dropped points, drawing with Atletico Madrid.
Real Madrid have the division's best defence, conceding just 15 goals in 23 league games, while Girona boast the best attack, with 52 goals.
Not only are Michel's side running Madrid closer than usual title challengers Barcelona and Atletico Madrid, third and fourth respectively, but they are playing the most dazzling football in Spain.
Thrilling to watch, with pace on the flanks and players flying forward with abandon, many would love them to do the almost impossible and become the first team to win La Liga outside of the 'big three' since Valencia 20 years ago.
To do that, earning at least a draw on Saturday seems imperative, but they will be without several key figures.
Michel is suspended after being sent off for complaints during the Real Sociedad draw, along with box-to-box midfielder Yangel Herrera and defender Daley Blind, both booked near the end of the same match.
Girona had a goal controversially ruled out against 'La Real' for offside 36 seconds before it was converted by Yangel Herrera.
While Barcelona coach Xavi Hernandez says referees are "totally" influenced by Real Madrid, Michel disagrees.
"I have the feeling that we are competing in the same conditions as the rest of the teams," said the coach last weekend.
"I don't see suspicious interference or strange situations."
Potential distractions have also appeared in the media in recent days, with Barcelona linked with playmaker Aleix Garcia and Manchester City poised to sign on-loan winger Savinho from parent club Troyes.
Girona and Troyes are both owned by the City Football Group, which some detractors believe takes away from the romance of the Catalan club's meteoric rise.
Madrid earned a comfortable 3-0 win when they faced Girona at the tiny 14,000-seater Montilivi stadium in September.
That remains Girona's only league defeat of the season to date and they responded by going 15 top-flight games unbeaten, claiming victories over Barca and Atletico.
Real Madrid hope centre-back Antonio Rudiger is fit to play after a knock - they used full-back Dani Carvajal in that position against Atletico last weekend.
La Liga's top goalscorers - Madrid's Jude Bellingham and Girona's Artem Dovybk - both on 14 strikes each, face off in another interesting subplot.
Despite Atletico snatching a late draw last weekend, Ancelotti said he was calm and happy with his squad's performances.
"We are leaders and we have another chance to make a statement win next Saturday," said the Italian.
"I'm calm, because the team is doing well... (this game) gives me a lot of confidence for the future of this league season."
