It is thought that preliminary discussions have taken place between Fernandes and the owners of the club, which was promoted to the Premier League last season.
QPR co-owner Bernie Ecclestone, who holds a 62% shareholding in the club, has previously said he may be willing to sell his stake for £100m.
It is thought that Ecclestone's business partner, Flavio Briatore, has an option to buy the shares should Ecclestone want to sell.
Briatore and Formula 1 supremo Ecclestone purchased the club in September 2007. Briatore vowed at the time they would be in the Premier League in five years' time. The club's other shareholder is steel magnate Laskshmi Mittal.
It is now understood the Ecclestone and Briatore have given the high-profile Fernandes the go-ahead to purchase the club
The football club made losses of £18.8m in 2008-2009 and £13.7m last year.
Fernandes, who is also the Team Lotus F1 boss, is the owner of the Air Asia airline and has previously claimed he made an offer to buy West Ham United.
QPR said it did not comment on speculation. Fernandes was unavailable for comment.