The 33-year-old insists that he wants to stay and fight for a place in Brendan Rodgers squad, but admits that he could yet move away from the club this summer
The Ivorian defender looked to be on his way out of Anfield after the Turkish club's president, Ibrahim Haciosmanoglu, claimed that a deal had been agreed with the former Manchester City and Arsenal man.
Toure made only 20 Premier League appearances in his first season on Merseyside, but despite realising his opportunities could be limited once again in the new campaign, the 33-year-old has rejected the overtures from the Super Lig club.
"Trabzonspor are interested in me, but I am happy to be a Liverpool player - especially as the coach [Brendan Rodgers] reiterated his confidence in me for what I bring to the group," Toure told Sport Ivoire.
"He wants to keep me to help Liverpool cope with all the competitions they are in. It's true that I have to look at all possibilities. If I sense there's a need to leave, then I will see.
"There's a possibility that I may need to drop into a lesser league to earn more playing time, but I am a battler and I have decided to stay at Liverpool. It's true that things can change at any time. For the moment, I repeat, I am at Liverpool and I hope to stay at the club.
"For now, Trabzonspor is a no. But in football, anything can happen.
"I know what to expect, but there will be lots of matches in the Premier League and Champions League, and I know I will have time to prove that I'm still hungry. I know I will not play every game, that's for sure."