Established Premier League sides Stoke City and Southampton have already been credited with holding an interest in Tripper, but Bournemouth feel he could be a vital addition to their ranks as they prepare to step up out of the Championship.
The right-back impressed during his first season in the top-flight with Burnley, despite the Clarets suffering relegation, and Bournemouth believe he could prove a valuable signing.
Eddie Howe has devised a system which encourages his full-backs to get forward, and Trippier's pace and energy makes him a natural fit.
The Cherries are said to be determined to bring in players with Premier League experience, and Trippier certainly ticks that transfer box.
Burnley are understood to be keen to keep hold of the full-back, so no club will have a straightforward route to securing his signature.
The Clarets see Trippier as one of their key players and a big bid would be required in order to move them to the negotiating table.