Turkish newspaper HaberTürk have stated that the Merseyside club have been monitoring Medjani in recent months and are preparing a €3 million bid for the 30-year-old.
“I am not happy at all with the operation”, Medjani told France Football.
I’ve never spoken to this site [which quoted me] and there has been absolutely no contact with Liverpool.”
The experienced defender’s contract with Trabzonspor runs until the summer of 2018.
Medjani was signed to Liverpool as a youth player from Saint Etienne in 2003 but left the club after several loan spells in France.
The Algerian international joined Trabzonspor from Monaco on a free transfer at the start of the season.
Medjani has previously played for Monaco, Valenciennes, Olympiacos, Ajaccio, FC Lorient, Liverpool, Metz and Saint Etienne.
The experienced defender has one assist and eight goals in 41 appearances for Trabzonspor this season.
Trabzonspor finished the league in sixth place and will not play European football next season.