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There is increasing confidence that Spurs will beat a number of their Premier League rivals and Serie A club Atalanta to the signature of the 18-year-old Senegalese, with Metz's president claiming to have a "verbal agreement" over a deal with Daniel Levy, the Spurs chairman.
Sarr broke into Metz's first team last season and the central midfielder has also been linked with Manchester City, Man United and Chelsea.
Metz's president Bernard Serin claims a deal worth more than £12million has been agreed, with Sarr set to spend this season back on loan at the Ligue 1 club.
"Nothing is signed, but I have a verbal agreement with the president of Tottenham", he told Amazon over the weekend.
"It is much more [than €15m], both on the fixed amount and the bonuses. Pape Matar must also be satisfied with the contract offered to him and this is not yet the case.
"There will be more discussions at the start of the week."
He added: "If the transfer is to Tottenham, he will be loaned to FC Metz [for the season]."
Tanguy Ndombele has asked to leave Spurs before the end of the month and faces an uncertain future, while the club has transfer-listed his France team-mate Moussa Sissoko.