The 33-year-old has a year left on his current contract after signing from Manchester City on a free transfer last summer.
He made 24 appearances for the Reds last season, including 15 starts in the league as Liverpool narrowly missed out on a first league title since 1990.
Liverpool boss Brendan Rodgers said Toure - part of the Arsenal 'Invincibles' side and a two-time FA Cup winner - was a key part of his plans for the new season, even if he was not a regular starter.
"Kolo has been an incredible player. We brought him in because he is a winner, an authentic winner," said Rodgers, talking at a news conference on Liverpool's pre-season trip to the United States.
"He's someone who doesn't play every single week but when he does play, he plays very well. Every day of his life in training, he gives his all.
"Players like Kolo and Steven Gerrard, the older statesmen of the team, have been absolutely first class. We're hungry and ambitious; we went close last year.
"That inspires us and gives us great motivation to go on this year. That is the beauty of this group of players - it's a very hungry group because that's what we're trying to bring in."
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Good grief, I missed this whilst on holiday. Let's get this straight: we've been offered a transfer fee for a player who was free last year, unlikely to play more than 10 games this year, been a key contributor to our defensive cockups and owngoals last year and sitting on high wages for another season. C'mon Brendan this isn't like eBay; we've only got one interested buyer....terminate the auction before we get left with dodgy goods again.- redped