The club were rocked on Thursday by a one-year transfer ban handed down by FIFA for alleged irregularities in the signing of minors.
Of more immediate concern for the 10-time European champions, though, is their pursuit of Atletico Madrid and Barcelona at the top of La Liga and, fortunately for Zidane, the Frenchman already has a hugely talented squad at his disposal.
Real Madrid hire Zidane as coach
Gareth Bale struck his second hat-trick in four games and Karim Benzema took his tally for the season to 18 goals in as many matches as Zidane got off a dream start against Deportivo just days after replacing the sacked Rafael Benitez.
"The change of coach has suited us well. Hopefully 2016 will be a great year for Real Madrid," said captain Sergio Ramos as he and three other Madrid players were named in the FIFPro team of the year in midweek, highlighting the quality that remains in the squad despite a disappointing year.
Zidane has a full compliment of players to choose from and Madrid will be out for revenge after being surprisingly held 0-0 by Sporting on their first match back in the top-flight on the opening day of the season.
Zidane to be 'top-class manager' - Houllier
Barcelona lead Real by two points and have a game in hand on their eternal rivals, but face a tougher task this weekend when they host Athletic Bilbao visit the Camp Nou.
The Basques denied Barca a clean sweep of silverware in 2015 on their last visit to the Camp Nou by sealing a 5-1 win in the Spanish Super Cup in August.
Lionel Messi will present his record fifth Ballon d'Or to the home fans before kick-off.
The Argentine wasn't given the night off as Barca eased into the quarter-finals of the Copa del Rey on Wednesday with a 2-0 win over Espanyol in the final of three bad-tempered Catalan derbies in the past 12 days.
Flying Welshman: Zidane urges Bale to maintain form
However, Neymar, Sergio Busquets, Andres Iniesta and Gerard Pique were all rested and will return, as will Luis Suarez, who was suspended for the visit to Cornella-El Prat.
League leaders Atletico were also hit with a 12-month transfer ban on Thursday, but that didn't distract Diego Simeone's men as they too eased into the Cup quarters with victory over Rayo Vallecano.
Los Rojiblancos travel to Las Palmas looking for their ninth win in their last 10 league games on Sunday, but Simeone believes there is still plenty of room for improvement from his young squad.
"We have managed to get results, but I have always had the sensation that the team could play better. The other day in Vigo, we managed both to win and play well. That is the growth that the team still has in it.
"We hope to be able to maintain that consistency because in the league season that is the most complex and difficult thing."
Valencia boss Gary Neville has a great chance to register his first La Liga win at the sixth attempt since taking charge last month when struggling Rayo visit the Mestalla on Sunday.
Neville has at least managed to negotiate Los Che into the quarter-finals of the Cup as they completed a 7-0 aggregate win over Granada on Thursday, but admitted he needs to pick up league wins quickly if he is to make a case for his contract to be extended beyond the end of the season.
"I don't shy away from what Valencia's expectations should be. In La Liga in the last few weeks we've not achieved the results we wanted to and I accept that we have to start winning games quickly."
Fixtures
Saturday
Sevilla v Malaga, Celta Vigo v Levante, Villarreal v Real Betis, Real Sociedad v Deportivo la Coruna
Sunday
Valencia v Rayo Vallecano, Real Madrid v Sporting Gijon, Las Palmas v Atletico Madrid, Getafe v Espanyol, Barcelona v Athletic Bilbao
Monday
Eibar v Granada
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