The report claims that negotiations are being held via İrfan Şahin who has a mandate to hold talks on behalf of the agent in Turkey.
The Black Sea Storm have struggled defensively this season and have made strengthening the back-four a priority going into the next league campaign.
Cissokho does however, have another two-years remanning on his current deal with Aston Villa but could be tempted to leave if the Premier League outfit get relegated at the end of the season.
Trabzonspor have been targeting Premier League players recently and also brought in Marko Marin on loan from Chelsea over the summer transfer window. The Turkish giants have a buy-out clause option but have yet to activate the clause.
Cisskokho has made 18 appearances in all competitions for Villa this season but spent the first half of the season on loan at Porto.