Reports in France claim the Super League side are willing to pay the former Paris St Germain, Arsenal and Real Madrid star 10.6 million euros (?9.17m) a year.
Anelka, who is available again for France selection after serving an 18-game ban for his part in the row which derailed Les Bleus' World Cup campaign in South Africa in 2010, is out of contract at Stamford Bridge next summer.
Chelsea boss Andre-Villas-Boas admitted last month he feared 32-year-old Anelka might not be interested in renewing his existing deal.
He said at the time: "It might not be the player's expectancy to renew (his contract).
"We will make our efforts for him to renew but Nico has his own decision to make and I am not sure he will be willing.
"Nico as a person is very, very happy and he still belongs to Chelsea in the last year of his contract."
Anelka has also been linked with moves to Major League Soccer with New York Red Bulls, Philadelphia Union and Montreal Impact as well as AC Milan.
Source: PA
Source: PA