Fans have taken to the winger, 18, who is excelling during his season-long loan from Tottenham. His pace, directness and trickery have made him a real asset in Danny Rohl's side.
His plan is to go back to North London and cement himself as a Spurs player and while there have been suggestions of another possible year at Ibrox, that is likely to be the extent of it.
This season, the league is Rangers' only chance of silverware after being knocked out of both cups. Moore wants to get his hands on it so he is remembered as a title winner, and not just another loan player.
Speaking on a Tottenham YouTube documentary about his time at Rangers, he said: "I want them to remember me not just as a young boy who came up. If we win something here, they will remember me as someone who helped keep pushing them to win the league.
"You see players do it who win trophies over and over again. I want to be someone who does that. That is my goal, to win trophies at the highest level possible and hopefully go on to play for my country.
"I have had a bit of everything already in four or five months and now we have a chance to go and win a title. At my age, that is what you want. You want to be involved in those games under that pressure. It has been perfect for me so far.
"Hopefully, when the season is over, we will be in the position to push for the title. There are going to be some huge games to play in and I am looking forward to it. I want to go back to Tottenham and hopefully get myself a place in the team."
Meanwhile, Moore has also opened up on his myocarditis care which kept him out for six weeks last season, but could have been so much worse.
He explained: "I was playing really well and started to find my feet in the first team just before the Galatasaray game. I trained two days before it and I was set to start or make an appearance in that game. I went for a driving lesson that night and all of a sudden I felt a bit of pain in my chest. The doctor called me in and said to forget about football for now.
"It came back that I had myocarditis, which is a virus that went to the heart and gave me pains. I was lucky that I caught it early because I am not sure what could have happened after that. From what I know, it is not something that can really reoccur. I was in bed for six weeks and was not allowed to do any exercise.
"There were a lot of rumors at that time and it was tough to deal with. Those six weeks felt like six months. Right now, I feel at my best and feel like how I felt when I first started playing at Tottenham. That is all done now and put behind me."