The former Chelsea winger suffered the setback during Real’s 1-0 defeat away to Levante on 22 February.
And HLN reports that he has been sent to the Carell Clinic in Dallas to be treated by a surgeon with experience of aiding in the recovery of basketball players.
Hazard is expected to go under the knife this week, possibly Thursday.
The injury continued a nightmare debut season for the forward in the Spanish capital, arriving just a week after his return from a three-month layoff.
Hopes are high that he will return to the pitch before the end of the season, allowing him to feature for Belgium at this summer’s European Championships.
Hazard has been restricted to just 15 games for Zinedine Zidane’s side this season since his summer switch from Chelsea.
His only goal for the club came in a 4-2 La Liga victory over Granada in October, while he has provided four assists.
Madrid agreed to a deal last July that could reportedly rise to £130 million, with the Belgian penning a five-year contract.
It ended a seven-year spell for the winger at Stamford Bridge, where he scored 110 goals in 352 games, winning two Premier League titles, the FA Cup, League Cup and two Europa Leagues in the process.
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