Arsenal are believed to be the favorites despite offers from Barcelona and MLS club Inter Miami.
Brazilian winger Willian wants a three-year contract and Chelsea have so far only been willing to give the long-serving player a two-year extension which seems unacceptable to him.
He's had a successful season for Chelsea this year, scoring 11 goals and supplying nine assists in 47 games across all competitions to help the club qualify for next season's Champions League.
ESPN Brasil add that Willian won't feature for Chelsea FC against Bayern Munich in the second leg of their Champions League round of 16 clash on Saturday night.
According to a report in Sky Sports, joining Arsenal will hand him a chance to work with fellow Brazilian Edu.
It is also believed that Willian wants to stay in the Premier League rather than going overseas.
Willian went on to firmly establish his place in the starting line up and continuously kept the likes of Andre Schurrle, Victor Moses, Juan Mata, Kevin De Bruyne, Mohamed Salah, Juan Cuadrado, Bertrand Traore and Pedro at bay under former Chelsea manager Jose Mourinho. Wilian is 31 and feels he deserves a substantial offer which could be his last significant one.
The Ghanaian has a £45m release clause in his agreement but Arsenal are unwilling to activate it, as they'd want to agree a decrease value and to involve Matteo Guendouzi in a offer.
"He is on an age where people will say he is in the twilight of his career but the way he players look after themselves these days, the way the live their lives, he will have at least another two seasons at the top level".
Chelsea are set to have a busy transfer window ahead.