The Italian replaces Zinedine Zidane, who left the La Liga club last month.
Former Juventus and Chelsea boss Antonio Conte is likely to be in the frame to replace Zidane, having walked away from Inter Milan on Wednesday after leading the club to the Serie A title.
Eden Hazard scored his first goal in almost three months while Karim Benzema bagged a brace as Real Madrid eased to a 4-1 win away to Alaves.
The win took the Spanish champions to the summit on 36 points, one ahead of second-placed Atletico who have three games in hand.
Atletico still lead the standings on 26 points, while Real climbed to third and closed the gap on their city rivals to three points, although Diego Simeone's side has a game in hand.
Goalkeeper Thibaut Courtois made a catastrophic error and record signing Eden Hazard suffered yet another injury as the defending champions suffered their third defeat in 10 matches.
Maradona had the self-belief, determination and sheer arrogance to keep on making the defenders look like fools.
Karim Benzema put Madrid ahead with a scorching strike from outside the area but Valencia replied with Soler's penalties and a bizarre own goal from Raphael Varane, inflicting a second defeat on Madrid this season.
Real Madrid clinched a record-extending 34th La Liga title with one game to spare by beating Villarreal 2-1 at home.
Real will clinch their first league title since 2017 with a win over Villarreal on Thursday or at Leganes on the final day of the season.