That's according to Matt Hughes of The Times, who reported both Gunners' contract rebels, Sanchez and Mesut Ozil, are focused on leaving the Emirates Stadium when the transfer window opens in July.
Metro's Tom Olver cited Hughes' report and mentioned the Blues as one of Sanchez's biggest suitors from the Premier League, although Arsenal would be less likely to sell their wantaway talisman to a domestic rival.
The other major English power in the hunt for the South American is Manchester City, and Goal's Sam Lee provided a recent update on their pursuit of Sanchez:
Chelsea are looking to build on manager Antonio Conte's Premier League triumph in his first season in charge, and the squad will need reinforcements ahead of its return to the UEFA Champions League next season.
Speculation has intensified regarding Sanchez's discontent in north London, although Goal's Chris Wheatley did provide a view of the winger looking at ease with manager Arsene Wenger following Saturday's FA Cup final win:
The Gunners pulled one over on Chelsea as they beat the Blues 2-1 at Wembley Stadium, where Sanchez again illustrated his importance to the Arsenal cause by scoring a controversial early opener.
Chelsea may count themselves as one of the few clubs able to finance a move for Sanchez, although Bundesliga champions Bayern present an allure that appears to have captured his attention ahead of the summer window.
Bayern midfielder and Chile international team-mate to Sanchez, Arturo Vidal, revealed he's been working to convince his compatriot to join him in Germany, per FourFourTwo:
"I said it was an opportunity for him to be on a big team. If you want to compare with the best, you have to go to the best team in the world."
City are strong competition in the transfer pursuit, however, as James Robson of the Manchester Evening News recently illustrated their big summer plans for Sanchez:
Willian, Pedro and star man Eden Hazard currently patrol the Chelsea wings, although Sanchez would be able to contend with any of that trio when it comes to fighting for his place in a Blues lineup.
Bayern may not be able to offer the same wage packet as their Premier League counterparts, but the desire to win major titles could tip Sanchez in favour of a move to Bavaria, rather than sticking around in the English capital.