Ancelotti came under fire for his side's dire display in their 4-0 El Clasico defeat to arch-rivals Barcelona. Real Madrid were outplayed and out-thought by the Blaugrana, leading many to call for the sacking of the Italian.
One of the names that has been bandied about as a potential replacement is that of Xabi Alonso. However, the 2010 FIFA World Cup winner has revealed that he is not attaching importance to the rumors.
The 40-year-old addressed the speculation in a press conference, saying:
"As I know how the world of football evolves and I know the club, I don't attach too much importance to it, I don't have much more to say.''
Xabi Alonso had an illuistrious playing career that saw him represent some of the biggest clubs in the world, including Liverpool, Real Madrid and Bayern Munich.
He spent five years between 2009 and 2014 at the Santiago Bernabeu, making 236 appearances in all competitions for the La Liga giants.
At his peak, Alonso was regarded as one of the best midfielders in the world. He was also established at international level, playing a key role in Spain's dominance between 2008 and 2012.
He ventured into management upon his retirement and was appointed as the manager of Real Sociedad B.
He has impressed in the dugout of the Basque side's reserve team and guided them to promotion to the Segunda Division in his second season.
This marked the first time the club was playing in Spain's second tier since the 1961-62 season.
His performances so far in his managerial career have seen him linked with moves to a bigger club, with Borussia Monchengladbach suggested as a potential destination last year.
Real Madrid's Clasico defeat has put Carlo Ancelotti under pressure
Carlo Ancelotti was a surprise appointment by Florentino Perez following Zinedine Zidane's departure last year. The Italian manager has hardly pulled up trees in the last few years, with his spell at Everton largely underwhelming.
Despite the initial skepticism, he set about his task with minimal fuss and is all but certain to guide Real Madrid to their 35th La Liga crown. He has also led the side to victory in the Spanish Super Cup.
They are also through to the quarterfinals of the UEFA Champions League, eliminating favorites PSG along the way.
Although they suffered an early elimination from the Copa del Rey, the biggest asterik came when Barcelona humilated Real Madrid in front of their fans.
The manner of the defeat was unacceptable to fans of the club, with the Catalans outplaying and out-thinking their rivals right on their own perch.
This has seen the pressure mount on Carlo Ancelotti and he will have to inspire a statement victory over Chelsea to calm the storm.