The 31-year-old is out of contract at Stamford Bridge in June and, as things stand, Willian will be able to walk away from Chelsea when his deal expires.
The Brazil international could put pen to paper on an extension until the season can reach a conclusion, but the two North London rivals are said to be eyeing up a swoop for the soon-to-be free agent.
According to The Telegraph, Arsenal and Spurs are prioritising swap and part-exchange deals as the two parties suffer the financial consequences of the coronavirus pandemic.
The report claims that both sides are interested in signing the Chelsea winger as a free agent this summer, while other Premier League top six sides such as Manchester United and Manchester City are unlikely be in such a financially desperate situation.
Willian has registered 59 goals from 329 games for Chelsea since his arrival in 2013, including five goals and five assists in the Premier League this term.