Isco, who was released by Sevilla in December after just four months at the club, looked set for a new challenge in Berlin when he reportedly completed a medical with Union.
However, the 30-year-old's move to the Bundesliga side collapsed on Wednesday (AEDT) over personal terms, with both parties blaming the other.
Former Real Madrid midfielder Isco may now have found another club, though, as discussions are ongoing with Super Lig side Konyaspor.
"That is correct. We are in a negotiating process with Isco," Akcan was quoted as saying by Spanish outlet AS.
"I can tell you that dialogues are going well. We are not yet sure if we have reached an agreement, otherwise we'd say so openly.
"We're doing everything possible to close the signing. We have until January 8, but I think everything will be resolved one way or another as soon as possible.
"Now we have the chance to close the signing and are positive of doing so."
Isco began his career with spells at Valencia and Malaga before spending nine years with Madrid, which he left at the end of last season for a short stint with Sevilla.
He made 19 appearances for Sevilla in the first half of the season, scoring once and providing three assists, but his contract was mutually terminated six weeks ago.
Serie A heavyweights Juventus and Napoli were previously linked with the 38-cap Spain international, while Konyaspor's league rival Fenerbahce is also reportedly interested.
Konyaspor is eighth in the Turkish top-flight, 13 points adrift of the European places.
Isco's former Sevilla team-mate Adnan Januzaj as also secured a move to Turkey.
The winger, who signed for the club on a free transfer in August, has joined Istanbul Basaksehir on loan until the end of the season after making just six appearances across all competitions.