The Belgian has struggled in his time with Real Madrid since joining the club in a £150m deal from Chelsea in 2019.
During his time with the Blues, he racked up 110 goals and 92 assists in 352 appearances, but he has failed to live up to those high standards in the Spanish capital.
In contrast, he has only been able to score seven goals and register 11 assists across the 73 games he has played for Real Madrid.
Hazard, who is under contract until June 2024, has also struggled for playing time after starting only three of Real Madrid's 22 competitive games this season.
Ancelotti included Hazard in the lineup for Tuesday's 1-0 victory over fourth-tier Cacereno in the Copa del Rey, but he was taken off in the 67th minute after failing to make a significant impact on the game.
With Hazard finding it tough to establish himself at Real Madrid, one of Turkey's biggest clubs are set to offer him way out.
According to Fichajes, Fenerbahce are interested in signing Hazard on a loan deal, and they would be prepared to pay the majority of his wages.
The report claims that the Turkish giants would be willing to pay €5m (£4.4m) of his current €6m (£5.3m) salary.
A move to the Yellow Canaries would see Hazard link up with other players who have previously played in the Premier League, including Michy Batshuayi, Josh King and Enner Valencia.
However, he is supposedly reluctant to agree to the move, and Real Madrid are happy for the player to make the decision rather than forcing him out of the club.
Although he is not keen on the loan proposal from Fenerbahce, a recent report indicated that Hazard was considering whether to move to the MLS at the end of the season.
Ancelotti has stated that he believes the former Chelsea player can be "important" for Real Madrid in the second half of the season.
The 31-year-old is currently competing with the likes of Karim Benzema, Vinicius Junior, Marcos Asensio and Rodrygo Goes for a place in the forward line.
Hazard will hope to be involved for Real Madrid's away La Liga meeting with Villarreal on Saturday.