Doak is currently starring on loan with Middlesbrough in the Championship.
The Sun says Liverpool are seeking £30m to sell the Scotland international this month.
Crystal Palace are also keen, though not at Liverpool's price, as such it is the Cherries who are now favourites in the battle for Doak's signature.
Interestingly, Doak was not in the matchday squad for Saturday’s 1-0 FA Cup defeat at home to Blackburn.
