The 27-year-old former England international was on loan at Cardiff City during the first half of the season, scoring five goals in 17 games.
He then returned to Elland Road earlier this month and, with the former Bolton star making only 5 appearances for the Whites this season, it was thought another move was in the best interest of the club and himself.
The Clarets have been in urgent need of a striker since selling Ade Akinbiyi to Sheffield United for £1.75m last week.