Teenage forward reportedly agrees to six-year deal with Spanish and European football champions, although French newspapers report that Monaco deny a deal is done.
Real Madrid agree world-record €180m fee for Monaco striker Kylian Mbappe
Real Madrid have reached agreement to sign Kylian Mbappe from Monaco for a world record €180 million (Dh770.4m), Spanish media reported on Tuesday.
Spanish sports daily Marca, citing sources close to the negotiations, said the teenage striker is expected to joining Madrid "in the next few days" on a six-year deal.
French newspapers Le Parisien and Nice Matin said Monaco had denied the report.
But Marca insisted that Real are set to pay between €150-160m with add-ons of between €20 and €30m, dwarfing the current world transfer record of €105m Manchester United paid to lure Paul Pogba from Juventus last year.
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Real are looking to fill the void left by Alvaro Morata who joined English Premier League champions Chelsea last Friday.
If he does arrive at Zinedine Zidane's European champions the 18-year-old striker will be on a net annual salary of €7m, Marca said.
Mbappe, under contract at Monaco until 2019, has been wooed by some of Europes' top clubs, including Monaco's arch Ligue 1 rivals Paris Saint-Germain.
Last week Monaco issued a warning to the likes of Real and PSG to lay off their player.
"Top European football clubs made contact with Kylian Mbappe and his entourage without our authorisation," Monaco said on their website.
The club said they wanted to remind these clubs that such actions are contrary to French and international regulations.
Mbappe scored six goals in 10 Uefa Champions League outings and 15 in Ligue 1 as he exploded onto the scene in the second half of last season.
On Monday Monaco lost full-back Benjamin Mendy to Manchester City in a world record £52 million (Dh249m) deal for a defender.
The principality side, who were the top scorers across all of Europe's top leagues last season with 107, also lost powerful midfielder Tiemoue Bakayoko to English champions Chelsea earlier this month, selling the France international for a fee of around £40 million.
Real Madrid's outlay on Mbappe, if confirmed, would almost match the total outlay spent by their opponents in a pre-season friendly in Los Angeles on Wednesday, Manchester City.
As well as Mendy, Pep Gaurdiola's side had earlier raided Monaco for midfielder Bernardo Silva (£42m) as well as signing Tottenham Hotspur for right-back Kyle Walker (£50m), versatile Real Madrid defender Danilo (£25m), goalkeeper Ederson from Benfica (£34m ) and Brazilian midfielder Douglas Luiz (£10m) from Vasco Da Gama.