The winger told Rangers News: "The manager has brought in a lot of players and for me it's been difficult to get in the side.
"I'm happy to stay here and fight for my place, I just have to impress everybody in training and improve my game. When I get my chance, and hopefully I will, I will need to take it."
Amdy Faye finds himself in similar circumstances to Burke, however the loan signing from Charlton has been slightly more active and has made five appearances.
The Senegal central midfielder is desperate to play more often and make more of a contribution to the club's season.
Faye, 30, said: "It's good to be at Rangers, but I need to play, you know. I came here to play, but right now I don't have the chance to."