Despite having been keen to remain at Chelsea, Willian announced on Sunday that he was leaving Stamford Bridge after a seven-year stay.
Keen to remain in London, the 32-year-old has been heavily linked with a switch to Arsenal on a free transfer.
According to the Evening Standard, the Gunners feel that they could be in a position to announce the addition of the Brazilian in the coming days.
The report suggests that terms have already been agreed, with the playmaker taking the opportunity to pen a three-year deal.
The pursuit of Willian has come at a time when Arsenal have recently announced that there will be 55 redundancies due to the financial implications of the coronavirus pandemic.