Mbappe is rated the best young talent in Europe following a sensational season which saw him score 26 goals in just 44 appearances.
The 18-year-old played a major role in helping Monaco win their first Ligue 1 title in 17 years and also helped the French side defy the odds to reach the semi-finals of the Champions League.
Mbappe showed his potential in the knockout stages of the tournament scoring six goals in just nine games and has attracted interest from a host of top clubs including Real Madrid, Manchester United and Manchester City.
Paul Pogba remains the world’s most expensive player after Manchester United forked out £89m to sign him last summer.
But reports in French newspaper L’Equipe claim Arsene Wenger is leading the chase to clinch his signature and Arsenal are prepared to pay a world record fee and make a €140m (Euro) offer.
The north London club mean business this summer as they look to make amends for a nightmare campaign which saw them fail to secure a top four finish for the first time in 21 years.
With uncertainty surrounding the future of Alexis Sanchez, Wenger is determined to bring another big forward into the squad and hopes the marquee signing of Mbappe would send out a big warning to their major rivals.
Speculation over a move for Mbappe has only has increased this week after Wenger was spotted in Nice along with chief executive Ivan Gazidis.
Arsenal fans will certainly be hoping that Wenger can win the race to sign the prolific forward and give them the extra quality in their forward line to compete for the title once again next season.