The 25-year-old striker is of interest to a host of Premier League clubs this summer including Newcastle and West Ham after Rangers were relegated as the league’s bottom side last term.
Sources understand Newcastle have made him their top target after the arrival of Steve McClaren, but Leicester are now attempting to bring him to the Midlands.
However, it is understood Rangers will not accept any less than £15million for a player who scored 18 Premier League goals last season – the fourth most in the division.
Austin has completed a remarkable journey from non-league football to the English top-flight and the international side; part of the England squad that beat Slovenia in their European Qualifier last month.
The striker joined QPR from Burnley in August 2013 after scoring 45 goals in 90 appearances for the Clarets.
He was instrumental when QPR won promotion to the Premier League in 2013-14, and has scored 38 goals for the club in all competitions.