The Cote d'Ivoire international signed for the Turkish giants on Monday, but the Chinese side which he joined in 2012 have insisted they will report the transfer to Fifa
The Istanbul giants confirmed the signing of the Ivorian icon on an 18-month deal on Monday, with the estimated transfer fee set at €6 million and a signing-on fee of €4m going straight to the veteran striker.
However, Shenhua, for whom the veteran striker signed after leaving Chelsea in the summer, have claimed that they will report the Turkish champions to Fifa over the transfer.
"The club are deeply shocked," a statement on the club's official website read.
"Drogba is still a Shanghai Shenhua member as the contract between the two parties is still within its period of validity," it added of the deal which saw Drogba sign a two-and-a-half-year contract last July.
"Shanghai Shenhua are ready to gather evidence and submit the findings to Fifa in order to protect its interests."
However, Drogba's Turkish representative Ceylan Caliskan has stressed that the striker has terminated his contract with Shanghai over a payment issue.
"Drogba terminated his contract with Shangai Shenhua on January 16. He had the right to cancel his contract if he went unpaid for one month, but he did not get his wages for three months. Shanghai might go to Fifa, but Didier can play on a temporary license," Caliskan told TRTSpor.
Drogba is currently at the Africa Cup of Nations with his national side, who eased into the quarter-final stage of the tournament with two wins in their first two group matches.