The Cherries have reportedly kept a close eye on the youngster, who has impressed for Paul Heckingbottom’s side in their return to the Championship.
Scouts have reportedly advised Howe to wrap up a summer deal, with Klopp considering selling the youngster to raise funds.
Kent has been a regular feature for Barnsley this season and has scored two league goals but managed just the one assist.
The 20-year-old could become the third Liverpool player to join Bournemouth after the Cherries signed both Brad Smith and Jordan Ibe from Anfield during the summer.
A move may depend on whether or not Bournemouth remain in the Premier League after a bad run of form has seen them dragged into the relegation battle this season, however, they may have done just enough to survive.