The Turkish club is leading the race to sign the former Arsenal man after he was given the green light to depart Anfield by Brendan Rodgers.
The 33-year-old joined the Anfield club on a free transfer from Manchester City last summer but the signing of Dejan Lovren and Brendan Rodgers’ determination to keep hold of Daniel Agger - despite reports linking the Dane with a move - have pushed Toure down the pecking order.
Trabzonspor is leading the race to sign the veteran center half and Goal understands the Turkish club is confident of concluding a deal for the former Arsenal star.
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Toure made 24 appearances for Liverpool last season but featured just once during the run-in between the end of February and May as the Merseysiders narrowly missed out on their first league title in 24 years.
Liverpool looks set to start the season with Lovren and Martin Skrtel at the heart of the defense but Rodgers appears keen to retain the services of Agger and insists he has yet to receive an offer for the 29-year-old.
Rodgers said: "I've seen some stories on that but, no, we haven't had any inquiries.
"Dan's still getting some work done on his knee, he's been a bit unfortunate since America. He's still getting treatment but we haven't had anything, no offers."