HITC Sport understands Charlton have rejected initial bid.
The highly-rated midfielder is being tracked by a number of clubs and the Addicks look to have a real battle on their hands to keep him following their relegation to League One.
Cousins has come through the youth system at The Valley, making his debut in 2013 and has since made over 130 first-team appearances for them.
He signed a four-year deal last year, but now he is keen to move back to the Championship and a number of clubs are interested in his services. Norwich City, Leeds United, Ipswich Town, Reading and Fulham are all understood to be keen.
However, HITC Sport understands that QPR have now made their move with boss Jimmy Floyd Hasselbaink keen on raiding their London rivals; however, their offer has been turned down.
It is expected that QPR will increase their bid in the coming week.