Liverpool boss Jurgen Klopp is also an admirer of the England international, who lifted the Premier League last term with the Foxes.
And according to the Daily Mail, Drinkwater has agreed terms on a new four-year contract.
However, as of yet, there has been no official confirmation from the club.
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Drinkwater's current contract expires in 2018.
He will follow team-mates Riyad Mahrez, Jamie Vardy, Kasper Schmeichel, Wes Morgan and Andy King, as well as manager Claudio Ranieri in committing their long-term futures to the club.
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