The 32-year-old, who was voted as the worst Premier League signing of the season in the annual Sports Mole Reader Awards, struggled during his first year at the Emirates, recording just one goal in 37 appearances across all competitions.
Willian still has two years remaining on his contract with the Gunners, but according to Sky Sports News, the winger wants a new challenge and Stamford Bridge is his number one destination this summer.
They also report that several other clubs, including David Beckham's Inter Miami side, are interested in the Brazilian, although he would prefer to stay and compete in one of Europe's top-five leagues.
Chelsea boss Thomas Tuchel already has a wealth of attacking options at his disposal who are capable of playing in Willian's position, including last summer's signings Timo Werner, Kai Havertz and Hakim Ziyech, as well as Mason Mount, Christian Pulisic and Callum Hudson-Odoi.
Before joining Arsenal, Willian made 339 appearances in all competitions for Chelsea during a seven-year spell with the club, recording 63 goals and 62 assists.