HITC Sport understands left-back will leave Leicester City.
Konchesky's contract at the King Power Stadium finishes later this month and the former England international has been informed he will not be getting a new deal.
The left-back spent this season on loan at Queens Park Rangers and Koncheskey started 33 of his 34 appearances for the club in the Championship.
Konchesky joined Leicester from Liverpool in the summer of 2011 and he played a key role in helping them win promotion to the Premier League in the 2013-14 season.
The former Fulham man then helped Leicester secure survival in their first season back in the Premier League before being allowed to join QPR last summer following the arrival of Claudio Ranieri as manager.
Konchesky impressed during his loan stint at QPR and a number of Championship clubs are thought to be ready to move for the defender on a free transfer this summer.
Konchesky is keen to continue playing on and is waiting to see what offers come his way before deciding where to move.