The only obstacle to the move is Bremen's asking price, but Leverkusen's general manager Wolfgang Holzhauser still hopes to negotiate a deal this summer.
"We want Sokratis and we're not making any secret about it," he said. "We are very far down the line, even with the player.
"We just have to negotiate with Werder because their demands are still too high for us."
Negotiations with Chelsea midfielder Kevin de Bruyne are not at such an advanced stage, however.
Leverkusen are keen on the Belgian, who has spent the season on loan at Werder Bremen, as part of a deal which could see Andre Schurrle join the Blues, but Holzhauser says the negotiations are currently on ice.
"Chelsea have always told us that he should go out on loan, but a decision will be taken when the new Chelsea coach is appointed," said Holzhauser to the Bild newspaper.