Liverpool were interested in Kelly before joining Bournemouth from Bristol City for £ 13million last summer.
And although they have only made eight appearances for the Cherries this season due to injury, the Reds were said to want to make an offer for the 21-year-old in the current transfer window.
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More Athletic says there is “no chance” Liverpool will travel for the England U21 international.
Michael Edwards, Liverpool’s sporting director, “was angered by the way the player’s agency performed last summer”.
The report claims that Jurgen Klopp is also interested in Norwich full-back Jamal Lewis, but the clubs are still quite a ways off when it comes to their ratings for the player.
The relegated side wants at least £ 20million for the defender, while Edwards has offered a £ 10million offer, with £ 8million up front and another £ 2million in add-ons .