The ex-Arsenal and England defender is reported to be the next name on the list of the mega-rich Super League club which signed Nicolas Anelka in December.
Shenhua has already acquired the services of former Chelsea and France international Nicolas Anelka and former Bordeaux manager Jean Tigana.
The big-spending Chinese club is also known to be pursuing Ivory Coast striker Didier Drogba.
However, on the topic of Upson and Drogba, Shenhua official Ma Yue told Reuters, "There is nothing confirmed. We are still in the midst of discussions."
Upson, 32, has endured a difficult campaign at the Premier League club having made just seven league appearances after joining in the summer as a free agent.
However, The Daily Mail is reporting Stoke boss Tony Pulis wants to hold on to Upson in the short term at least, after Robert Huth's appeal to overturn his red card from the weekend's loss to Sunderland failed.