The 19-year-old Scotsman has been an important player for the Serie A outfit this season, scoring five goals and providing one assist in 36 league appearances.
Mikel Arteta is believed to be on the lookout for a new left-back this summer, as Kieran Tierney continues to struggle with injuries, while Nuno Tavares has failed to hit the heights expected at the Emirates Stadium.
Arsenal and Napoli are among the clubs to have allegedly entered the race to sign Hickey, who has just over two years remaining on his contact.
However, the Evening Standard claims that Napoli are on the verge of signing Getafe left-back Mathias Oliveira, paving the way for the Gunners to move for Hickey.
Hickey will be looking to add to his two senior Scotland caps when he joins up with the national team ahead of next month's World Cup playoff against Ukraine.