It was made clear by Arsenal manager Arsene Wenger that he would listen to offers for the injury-plagued star, but no deals were agreed.
Wilshere has had a torrid few seasons due to injury setbacks, but things appeared to be looking up when he made 27 Premier League appearances during a loan spell at Bournemouth during the 2016-17 campaign.
However, the stint ended in disappointment when the England international broke a bone in his leg and was forced to return to the Emirates for treatment and rehabilitation.
The 25-year-old was wanted by Trabzonspor, but the Turkish outfit failed to get a deal done before the transfer deadline on August 31.
"I held direct talks with Jack Wilshere," Turkish-Football quotes Usta as saying. "We wanted him on loan and were close to a deal but the move stalled at the last moment."
Wilshere has featured twice for the Arsenal reserves this season, but is yet to make a top-flight appearance.