The club have recently confirmed that they have signed out-of-favour striker Nicolas Anelka and are rumoured to be paying the French striker a whopping €9.425 million per year.
Shanghai Shenghua director Zhou Jun announced that the club will be willing to spend more to improve on the club's 11th place in the Chinese League last season.
With Didier Drogba's contract at Stamford Bridge running out at the end of the season, the Chinese club are interested in luring the Ivorian to the Far East to continue his strike partnership with Anelka.
"Drogba is an excellent player," Zhou told Reuters. "We got in touch with him two weeks ago.
"From our club's perspective, we have this to say: If he is willing to come, we will definitely welcome him.
"It's like with the opening up of China. We needed to bring in the good stuff from foreign countries for us to learn from."
Shanghai Shenhua are not the only Chinese team to be interested in the services of Drogba. Newly-promoted Dalian Aerbin have also indicated that they wish to bring the 34-year-old striker to China as well.
Dalian's general manager was quoted in the Chinese press as saying: "Money is not the problem. Drogba is still one of the most popular soccer stars in the world, though he will be 34-years-old.
"We have talked a lot with Drogba's agent and promised to provide him with a three-year contract.''
Drogba has been linked with a move to the MLS ever since it was apparent that he is set to leave Stamford Bridge.