The Chinese outfit remain adamant that the striker has an ongoing contract with Shenhua, and have urged the Chinese football association not to release the player's transfer papers
The 34-year-old was set to continue his career at the Istanbul powerhouse after signing an 18-month deal with Galatasaray in the January transfer window.
However, Shanghai Shenhua have contested the transfer as they claim Drogba is still under contract with the Chinese side.
The attacker's Turkish representative stated earlier this week that Drogba had rescinded his contract due to Shanghai's failure to pay him for three months, but Shenhua are adamant that they fulfilled all their obligations.
The Shanghai side have provided the Chinese football association (CFA) with the necessary papers to prove that they did pay Drogba all the wages owed, and have urged the CFA not to release the player's international transfer certificate.
Drogba would not be eligible for Galatasaray in official games if the CFA does not provide the Turkish giants with the international transfer certificate.