Both Mbappe and Hazard are valued at around £100m ($128m) by their respective clubs and the Spanish capital club are keen to free up funds by allowing Bale to leave the club during the summer transfer window.
Citing sources in Spain and Manchester, the Independent reports that Real will negotiate with the 20-time English champions about signing the Wales international, who has struggled with injury in the recently concluded campaign. It is claimed that they will demand in excess of the £85m that they paid Tottenham Hotspur to sign him in 2013.
Bale has managed just 19 appearances in the La Liga this season owing to a number of injury troubles. He was out from the end of November last year until mid-February in 2017 with an ankle injury. He returned for 10 games before he suffered a calf injury that ended his domestic season pre-maturely. The Welsh attacker has returned to training and is in contention for a place on the bench when Real take on Juventus in the Champions League final in Cardiff on Saturday (3 June).
The 27-year-old has lost his place in the starting line up to Isco and it is claimed that the team look a more cohesive unit without Bale and hence the Spanish champions are willing to allow him to leave in the summer. Moreover, they are keen to bring in another high profile signing which will require them to raise funds.
Mbappe looks to be the more viable option for Real this summer after Hazard committed his future to Chelsea, by stating that the will remain in Stamford Bridge for at least two more seasons. The Monaco forward, on the other hand, has indicated a willingness to leave during the transfer window, but the Principality club seem reluctant to sell their young star after having reportedly rejected a £103m bid from the 11-time Champions League winners and more recently an £87m bid from Arsenal.