The 25-year-old's contract expires at the end of the season and he has been linked with a move away from the Eredivisie club over the past few months.
Newcastle United were believed to have been eyeing a deal for the Brazil-born stopper last summer, while Fulham were also linked with a late deadline day swoop in August.
Last month Anzhi made an offer for the player's services as they tried to find a replacement for QPR-bound Christopher Samba before the close of the Russian transfer window on February 27.
However, it appears Douglas, who is now a Dutch citizen, is determined to make the move to Serie A in the summer, with Inter seen as the frontrunners for his signature.
"It is good that a top club like Anzhi made an offer to Douglas, but he wants to play in Serie A," his representative Marcos Paulo Ribeiro told Russian newspaper Izvestia.
"And when Inter showed interest in the player, we decided to stop negotiations with the Russian club and wait for the summer transfer market."