The 33-year-old has two years remaining on his contract at Emirates Stadium but is keen to leave after a disappointing first season having joined the Gunners from Chelsea on a free transfer last summer.
Arsenal are seeking to reduce their wage bill and trim their squad after committing more than £130m on new signings in the current window and sources claim talks have taken place over a deal which may not involve Corinthians paying a fee.
Willian earns a basic £100,000-a-week salary, but has found opportunities hard to come by under Mikel Arteta. The Brazilian missed Arsenal's opening two Premier League defeats to Brentford and Chelsea after testing positive for Covid-19.
No agreement has yet been reached between the two clubs with Willian thought to ideally want to stay in Europe, but the move is under serious consideration given how badly his career has stalled in north London.