The Chile international does not believe he is inferior to any other player and feels his abilities match those of the two most recent Ballon d'Or winners
Alexis was a team-mate of Messi's at Barcelona, but departed Camp Nou for the Premier League ahead of the 2014-15 season in search of regular starts.
The Chile forward has become a firm fan favourite at the Emirates Stadium after scoring 30 goals in 68 league appearances for the Gunners.
Messi and Real Madrid rival Ronaldo are widely considered as the best two players on the planet and have held a monopoly over the Ballon d'Or award for the past eight years.
But Alexis is confident that he can be considered on their level.
In quotes published by Sport, he said: "I have reached a level where I can compete with great players.
"I do not feel inferior to anybody.
"I liken [my qualities] to Messi and Ronaldo. I have the same abilities as them."
Alexis won Liga and Copa del Rey medals with Barca and also has an FA Cup triumph to his name with Arsenal.
Arsene Wenger's side return to Premier League action following the international break against Southampton on Saturday.