Willian reportedly had little interest in leaving Chelsea until it became apparent that he would not receive a new three-year deal.
Last week, Arsenal confirmed that they had won the race to sign the 32-year-old on a free transfer after his exit from Stamford Bridge.
However, according to ESPN, the Brazilian pushed hard to convince Chelsea officials to meet his contractual demands.
Willian had made no secret of his desire to remain at Stamford Bridge, providing that he was given terms which lasted past 2022.
Nevertheless, it is claimed that the playmaker was left feeling "discredited" after Chelsea failed to reward him for an impressive seven-year stint in West London.
Manchester City, Manchester United and Bayern Munich are said to have also made an offer for Willian's services.
