The 25 year old only moved from Real Betis in a €2.9m deal back at the start of July, but has already begun to impress visiting scouts during the first few months of the season.
In addition to the Gunners, it is being reported that West Ham United have also been watching the former Italian under 21 international. The full back has so far played 12 games in all competitions, providing one assist.
Piccini started out life at Fiorentina before a number of loan moves. His spell at La Liga side Betis turned into a permanent deal in 2015 and he spent two seasons with the Spanish club.
This season, under the management of Jorge Jesus, he has begun to develop his game, helping Sporting to an unbeaten start in the Primeira Liga, with his side conceding just four times in eight league matches. He also played the full 90 minutes against Barcelona in the Champions League, where they restricted the Catalan giants to a solitary goal; an own goal by former Liverpool defender Sebastian Coates.