Simpson has been an unused substitute in Hull's last two games following the recent arrival of strike pair Matty Fryatt and Aaron Mclean, but is pushing for a recall after scoring twice in a behind-closed-doors midweek friendly against Leicester.
The 22-year-old said: "I want to play, like with every game, and especially against my old club it would be nice to nick a goal as well.
"QPR have done very well this season. Last season, they started well and then were battling against relegation, so to maintain their place at the top shows how well they've done this year."
Simpson believes the extra competition for places at Hull will bring out the best in him.
He added: "I've always welcomed competition because I feel that can only make me a better player."