Reports over the weekend had suggested the Reds were considering a £20million summer move for the highly-rated 21-year-old.
Cook skippered England U20s to World Cup glory in South Korea and was included in the senior squad for the friendly against Brazil during the autumn.
The defensive midfielder has been a regular for Bournemouth this season with his continued progress set to be rewarded with the offer of a new contract at the Vitality Stadium.
However, Cook – who moved from boyhood club Leeds United in July 2016 in a deal that could eventually be worth £10m – is not on Liverpool's radar.