The Gunners have been targeting Mbappe for a while now with manager Arsene Wenger reportedly ready to break the world-record fee to sign the Monaco striker who is open to a move to the Emirates Stadium this summer.
Most recently, the 65-year-old also stepped up his pursuit of Mbappe by making a personal phone call to the 18-year-old and touching upon how he can manage the rest of his career.
However, Real Madrid are said to be leading the chase and should Arsenal miss out on the France international, they will attempt to sign another Frenchman in Martial.
According to the Daily Mail, Wenger is ready to bid £40m ($51m) for the out-of-favour Martial who found his game time drastically reduced at Old Trafford under Jose Mourinho.
The former Monaco player had a solid debut season with United in 2015/16, scoring 11 league goals in 31 games.
However, Martial only managed four league goals in 24 games this past season, having started just 18 league games.
While the personal animosity between Wenger and Mourinho makes a deal between the two highly unlikely, it is said that the north London club will instead reach out to the United board with the hope that they would accept a big fee for a player not expected to start many games.
If a deal is to be successful, Martial could find himself forming a new partnership with fellow Frenchman Alexandre Lacazette, who Arsenal are close to signing in a £44m ($56m) deal.