The 22-year-old has emerged as one of the most coveted midfielders in Europe after an impressive season for the Ligue 1 leaders.
And French magazine France Football claim Wenger met with Bakayoko in a Paris hotel in November last year.
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Monaco midfielder Tiemoue Bakayoko
But the report says the Gunners boss was unable to persuade the player to join him.
Arsenal are likely to be busy in the summer transfer window after a disappointing season and contract doubts over several players.
Tiemoue Bakayoko with France team-mate Adrien Rabiot
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The reports adds Chelsea boss Antonio Conte is determined to capture Bakayoko and partner him with N'Golo Kante.
Monaco are said to want around £52m for Bakayoko, which would be a significant return having bought him for just £7million three years ago.
Bakayoko could be among a number of Monaco players to leave in the summer with team-mate Kylian Mbappe, Thomas Lemar, Fabinho, Bernardo Silva and Benjamin Mendy all linked with Europe’s best.