Robins boss Gary Johnson has targeted 26-year-old Carle, who is currently playing in Turkey.
"He will add quality to our squad and give me extra options because he can play anywhere across the midfield and also up front.
"We are delighted to now be one of three clubs vying for top position in the Championship, but that won't stop me trying to bring in some new faces.
"We know what we want and what is out there, but I can't be firm on any deals as yet."
Robins are coughing up £500,000 for Carle and Genclerbirligi will get an extra £200,000 if the Robins are promoted. Carle failed to make an impact in his six months at Genclerbirligi and wasn't under consideration by management for the second-half of the season.