With the Reds persisting with their efforts to sign Croatia defender Dejan Lovren from Southampton, Toure could soon be surplus to requirements at Anfield.
The Reds only signed Toure on a free transfer last summer—after his contract with Manchester City expired—but the 33-year-old appears to have served his purpose.
Should Liverpool sell Kolo Toure?
Pushed out of the starting line-up at City during the 2012-13 season, Toure went on to make 15 Premier League starts for Liverpool last term but eventually fell behind Daniel Agger and Mamadou Sakho as the preferred partner for Martin Skrtel.
Tellingly, Toure featured in just one of Liverpool's final 11 games as the club made their challenge for the Premier League title, per Soccerbase.
Manager Brendan Rodgers put his faith in other options, sending a clear signal that the Ivory Coast international can expect to spend much of the forthcoming campaign on the bench.
The former Arsenal defender can now class himself as a veteran centre-back, but the commanding performances of old seem to be long gone.
In fact, he was responsible for dropping two valuable points against West Brom last season when his poor pass was jumped on and converted by striker Victor Anichebe. Liverpool eventually lost the title by two points.
Only 10 days later, Kolo was caught in the eye of yet another storm. In what can only be described as comedic, Touré got Kieran Richardson's seemingly innocuous cross completely wrong and sliced the ball backwards and past (Simon) Mignolet to gift Fulham the lead in what was a crucial game for the Reds.
Toure only has 12 months remaining on his contract, but it would make sense to offload the defender now.
Brendan Rodgers has already taken his spending towards the £60 million mark, per the Daily Mail, and is still hoping to add Lille striker Divock Origi and Sevilla defender Alberto Moreno in addition to Lovren.
Money is not a problem with Uruguay striker Luis Suarez heading to Barcelona in a £75 million deal, but space in the squad is.
The continued development of young defenders such as Jon Flanagan, Andre Wisdom and Martin Kelly means Rodgers has plenty of talent to turn to as he copes with the added fixtures of the Champions League this season.
It would suit both the club and the player if a deal was struck with Trabzonspor for Toure.
Toure, who already has Premier League and FA Cup winners medals with Arsenal and City, can't really turn down the chance of first-team football in his latter years, while Liverpool could count one more player off the wage bill.