Goal.com earlier reported the 12-time European champions will battle it out with Manchester City in signing the France global.
The Sun report that the Parisians, who recently pulled off the record breaking signing of Brazilian superstar Neymar, are closing in on a move for their latest signing and fellow countryman, who can operate at right back or defensive midfield.
Sanchez is into the final 12 months of his current deal at the Emirates and as it stands can leave on a free next summer but is still attracting significant offers despite Arsenal's reluctance to sell.
After allaying fears that Emery's system is not suited to his style, L'Equipe - who confirm the agreement between Mbappe and PSG - say the French starlet was further won over by the capture of Neymar, who he is desperate to play alongside next season.
Zinedine Zidane has the services of Cristiano Ronaldo, Gareth Bale and Karim Benzema to lead his side's attack, while Isco has also impressed in the attacking position. The deal is not completed, but talks are quite advanced and there could be news very soon regarding the future of one of Europe's brightest young players.
The 18-year-old was one of the star performers in Leonardo Jardim's side as they went on to win the league for the first time since 2000.
PSG are now hoping their £360m front line can help them dominate Ligue 1 and the Champions League.
Mbappe scored 26 goals in 44 appearances for Monaco in all competitions last season, earning huge praise and getting comparisons with Thierry Henry.