The 32-year old Frenchman continues to be left out of Andre Villas-Boas' starting line-ups at Stamford Bridge with just three starts and six substitute showings in the Premier League so far this term.
Anelka's future in Southwest London has been questioned for some time and with Villas-Boas ready to move on some older players in January, the former Arsenal, Liverpool, Manchester City and Bolton man could be on his way to a new club.
There is some interest in Anelka with the likes of Italy's AC Milan, Russia's Anzhi Makhachkala and some clubs from North America's MLS and the Middle East all in the queue but Shanghai have now joined the race with a club official confirming the curiosity to DF Daily.
"It is so difficult. We actually asked about Anelka," said the Shenhua spokesman.
"We also know he could leave the Blues as a Bosman player next summer but there are so many clubs interested in him.
"AC Milan, Russian clubs and some Gulf clubs. If we want to sign him finally, [his contract] would cost plenty."