Lancashire-born Pugh, 31, is Bournemouth’s longest-serving player, having joined from Hereford in 2010 for just £60,000.
He has made 274 appearances and was part of the Cherries side that rose through the Football League to reach the Premier League in 2015.
But the wingman has found opportunities hard to come by this season, making just three appearances for Eddie Howe’s side.
Despite Pugh’s arrival, Hull remain intent on keeping star wingers Jarrod Bowen and Kamil Grosicki at the club by the close of the transfer window.
Hull have also been linked with a move for Pugh’s team-mate Tyrone Mings, but Aston Villa, West Brom and Nottingham Forest are also keen.
Meanwhile, talk of a Tigers bid for Rotherham United striker Michael Smith appears wide of the mark.