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The Blancos must raise funds through a number of sales
The Blancos are hoping to raise up to €150 million (£134m/$183m)in sales to fund the move, with Mbappe yet to sign an extension of his PSG contract that expires in 2022.
Gareth Bale, Isco, Marcelo, Dani Ceballos, Luka Jovic and Brahim Diaz are all said to be available.
The 22-year-old has become a key figure for the Bundesliga side, tallying fivegoals and twoassists this season.
Juventus and Leeds are also watching Gonzalez, who has a contract with Stuttgart through 2024.
Manchesster City midfielderFernandinho is undecided over his future, according to The Telegraph.
The 35-year-old's City contract expires at the end of the season and he could return to Brazil to play for his former clubAtletico Paranaensein the summer.
ButFernandinhocould be persuaded to spend one more season with City if the club offer him a new deal.
Catarina Macario has said a chat with star forwardAda Hegerberg helped convince her to sign with European championsLyon.
Macario would have almost certainly been the first pick in Wednesday night's NWSL draft, but the former Stanford University star instead opted to begin her professional career in Europe.