The 35-year-old's contract at the Turk Telekom Arena expires in June, but the player is beyond Peixe's financial budget.
The former Chelsea striker joined the Istanbul club from Shanghai Shenhua in January last year but has been linked with a move away from Turkey after entering the last six months of his contract.
Reports in Brazil claim Santos offered Drogba a short-term, two-month deal, only for the player to turn down that proposition, with Rodgrigues admitting the move was out of the financial reach of his club.
“Talks happened, but the money is very high,” he told reporters. “It is a dream of the fans, but Santos has no condition to hire. We would love to [sign Drogba], but there is no possibility.”
The 35-year-old's 18-month deal at the Turk Telekom Arena expires in June, with Drogba reportedly earning 10 million euros over the course of that contract.