The Chilean international has just under 18 months left on his contract with the north London club, giving the Serie A champions confidence that they can secure a cut-price deal for a 28-year-old who has already shone in the Italian top flight with Udinese.
Friday's Corriere dello Sport claims a €30million (£25.7m) bid has been made but The Independent understands no concrete offer has arrived with the club. Rather, the outline of a deal has been proposed to intermediaries working with the Sanchez camp, who in turn have indicated a willingness to move to Turin.
Even shorn of their leverage by Sanchez refusing to sign a new deal and just 12 months remaining on the contract, Arsenal would not be willing to lose their most prized asset for such a low fee. Some at the club even suggest that, should Sanchez continue to refuse a new deal, he will be retained for next season and allowed to walk away on a Bosman.
That strategy would, however, also give Arsenal extra negotiating time in trying to hammer out a long-term deal. Even sources close to the player's camp acknowledge that the situation could change and that no door is closed on the Gunners.
That said, Arsenal have shown an unwillingness to get close to the £300,000 wages that Juve and Paris Saint-Germain would happily agree to. The Old Lady have received all the encouragement they needed to make Sanchez their number one target and his signing would, a year or two down the line, allow them to cash in on superstar-in-waiting Paulo Dybala, who recently signed a contract extension but is being courted by Real Madrid and Barcelona.