In response, the Serie A side proposed a swap deal which would see Gunners attacker Pierre-Emerick Aubameyang head in the opposite direction.
Icardi, one of the most prolific strikers in Europe in recent seasons, is currently looking for a new club after falling out with the San Siro’s side’s regime.
The Argentine hitman did not join the Azzurri on their pre-season tour in hope of finding a solution to his scenario.
Inter want to cash in on the 26-year-old, who has scored an impressive 124 goals in 219 appearances for the club.
And it seems that Arsenal believed they could potentially snap Icardi up for a bargain price.
New Inter coach Antonio Conte has informed the player that he is not in his plans next season.
The ex-Chelsea boss has designs on bringing in Romelu Lukaku from Manchester United, although the club’s first bid of £54m was rejected.
According to Calcio Mercato, Arsenal decided to test the water by making tentative enquiries with Inter for Icardi.
But the Serie A giants refused to consider a cash sale and were only interested in a straight swap for Aubameyang.
The Gabon star played a big role under Gunners boss Unai Emery last season, forming a potent partnership with Alexandre Lacazette.
Whether he would have been interested in a move to Inter seems doubtful, but Icardi rejected the chance to join Arsenal anyway, thus killing any hope of a deal.
The Argentina international has openly expressed his desire to stay in Milan.
He has however been linked with a move to Manchester United and Juventus.
Emery is still aiming to complete deals for William Saliba, Kieran Tierney, Dani Ceballos and Wilfried Zaha in the upcoming weeks.
The Emirates outfit are currently enjoying their pre-season tour of the USA, having won all three of their games so far.
Seven of Arsenal’s eight goals against Bayern Munich, Fiorentina and Colorado Rapids have been scored by players under the age of 19.