Chelsea hoped that another club might attempt to buy Conte out of the final year of his deal, but possible openings at Paris Saint-Germain and Italy national team never materialised.
Real are said to be considering Hazard as a replacement for Cristiano Ronaldo after the five-time Ballon d'Or victor joined Juventus this week.
The Belgian captain is a known admirer of Zinedine Zidane who stepped down as Real boss barely days after winning the Champions League for a third consecutive time.
The reports claim that Madrid have narrowed their search and have fixated on Eden Hazard as their #1 transfer target following Ronaldo's departure to Juventus.
The Chelsea and Belgium forward has said that he is happy at Chelsea however - but suggested it would be a "dream" to play for Real Madrid.
Time for a new era, says Ronaldo - Portuguese star explains Juventus move
The Belgium captain has recently been dumped out of the World Cup by France after a 1-0 loss in the semi-finals. And it is that kind of ambition that will keep the Belgian in London, who wants to win the Champions League .
According to Spanish daily Mundo Deportivo, Barcelona believe it would be too costly a deal to pull off and believe signing Hazard this summer is an unviable option for the club.
"He's probably one of the best footballers in one-v-one situations".
Real Madrid will undeniably need a marquee signing this summer to make up for Ronaldo's absence.
Hazard has won the Premier League title twice with Chelsea, in 2014-15 and 2016-17, since joining from Lille six years ago.
These rumours certainly seem to be gathering momentum with each passing day. "I've seen an incredible, incredible journey in his career".