The Chinese outfit only signed Drogba from Chelsea last summer and have been left angered by the player’s defection.
“The club is deeply shocked,” they said in a statement on their website.
“Drogba is still a Shanghai Shenhua Football Club member as the contract between the two parties is still within its period of validity.
“The Shanghai Shenhua Football Club is ready to gather evidence and submit the findings to FIFA in order to protect its interests.”