The 25-year-old's contract with Twente expires at the end of the season and he has long been linked with a move away from the club.
Newcastle United and Fulham are both reportedly interested in the defender. Douglas has already turned down a transfer to Russian side Anzhi Makhachkala.
Inter Milan are now reportedly leading the race to sign Douglas.
"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."