Along with Hazard, Belgian team-mate Thibaut Courtois is also debating a new deal at the English club, being also linked with a move to Los Blancos.
"He's a player full of confidence at the moment, he's in the form of his life", Gerrard said on BT Sport.
His teammates were anxious by Hazard's words after the game, with his comments signalling that he is becoming frustrated playing in the false nine position in Chelsea's biggest games and believe he wants to play for a club that show ambition against Europe's best.
But, with Chelsea faltering in a Premier League title defence once again, and highly unlikely to win a trophy this season, Hazard appears set to call time on his spell at Stamford Bridge. It's the second time in as many weeks the Belgian has been openly critical of boss Antonio Conte's tactics after he was chosen to play as a false-nine.
Madrid and manager Zinedine Zidane are known to be admirers of Hazard and view the 27-year-old as a potential long-term replacement for Cristiano Ronaldo at the Bernabeu. However this season ends up for Chelsea, Hazard (and others) should not be shirking from the challenge of returning Chelsea to previous glories next season.
Meanwhile, Harry Kane and Mohamed Salah have been on a rampant scoring run this season and are leading the Premier League goalscoring charts.
"It only went better at the end of the game". Although Real Madrid have found fluency in attack of late, the need to bolster Zidane's options upfront seems to be paramount.
Reports that the Belgium worldwide is holding out for a move to Real Madrid continue to spread around the rumour mill.
Hazard's departure would be a huge blow to the west London club, but how would Chelsea line-up if the Belgium star leaves?
"He's the star player at Chelsea, but there has always been talk of him moving on", Carragher told MNF. It now remains to be seen if Los Blancos do make a concrete offer for the Chelsea talisman.