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.
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."