Arsenal were pushing to sign Willian on a free transfer this summer.
The Brazilian is out of contract when the Premier League season concludes and is not signing another one with Chelsea.
He is still being linked with a move to the Gunners, but their present interest in him is unclear.
The Mirror is reporting that before the coronavirus pandemic, Arsenal were ready to offer Willian £250,000-a-week.
However, the club are likely to spend less on both wages and transfer fees when the transfer window opens.
The club are also being linked with a loan move for Barcelona's Philippe Coutinho.