QPR boss Harry Redknapp is keen to bolster his attacking options and has stepped up his interest in Austin after missing out to Norwich for Gary Hooper.
Redknapp is a long-term admirer of Austin and talks between both clubs are understood by Sky Sports to be at an advanced stage about a deal for the 24-year-old.
Austin, who scored 28 goals last season for Burnley, saw a proposed move to Premier League new boys Hull City fall through earlier this summer.
Since the breakdown of the Hull move, Austin has gone on to play in the last four of Burnley's five friendlies and scored twice against Sparta Rotterdam.
Burnley are resigned to losing their star striker with Austin entering the final year of his contract at Turf Moor and QPR are hoping to win the race for the former Swindon hot-shot.