The club's veteran defender could be set to leave the Premier League for Turkey after 12 years in England.
Toure made 24 appearances for the Reds last season, but struggled to replicate his strong form at Arsenal and his first couple of years at Manchester City, both clubs he won the Premier League at and went on to captain.
The 33-year-old Ivory Coast international has featured regularly for Liverpool in their summer friendlies, skippering the side at times, but looks like he may have played his last game for the club, and is set to head to Turkey next week to finalise a move.
The Super Lig side finished 4th last season, qualifying for the Europa League once again, and had seen an initial bid rejected by Liverpool for the defender.
If Toure signs for Trabzonspor he will be linking up with fellow Premier League title winners Jose Bosingwa and Florent Malouda, both players that won trophies at Chelsea, while Paraguayan goal machine Oscar Cardozo is the big name arrival this summer, having left Benfica after seven years.
Former Liverpool defender Carl Medjani, who failed to make any appearances for the Reds in a three year spell as a youngster, has also signed for the club, meaning Trabzonspor could be set for a former Anfield central defence in time for the start of the season.
Whether Toure's likely departure will mean Reds favourite Daniel Agger remains on Merseyside will be an interesting side story from the deal, with the Dane continuing to impress last season despite his niggling injuries and slight loss of favour under Rodgers.
Of course, Dejan Lovren has come in at the back for £20 million from Southampton, and looks set to partner Martin Skrtel in the centre of defence, while Liverpool also have French international Mamadou Sakho on their books. These three players alongside Agger would be sufficient cover for the Anfield club, but if the former Brondby man is sold, another centre back will surely have to be brought in, unless Rodgers puts his faith in young Portuguese defender Tiago Ilori.