The 19-year-old forward made a scoring debut in the 2-0 home Scottish League One win over Dunfermline in March and featured in the Gers' next three games.
However, he was left on the bench for the Ramsdens League Cup final against Raith Rovers at Easter Road last week and for the William Hill Scottish Cup semi-final defeat to Dundee United at Ibrox on Saturday.
Gallagher, who signed a two-year extension to his contract three weeks ago, featured for Rangers' Under-20s in the Youth Cup semi-final win over St Mirren on Sunday but is hoping Ally McCoist gives him more game time in the final weeks of the campaign.
Ahead of the League One clash with Forfar at Ibrox on Tuesday night, he said: "To be a regular in the first team is my target.
"Things are going well the way they are but I think I can be a bit greedy and hope for a bit more.
"I would love to play every game until the end of the season but that is not the way things work sometimes.
"I will take whatever I am given and I will be happy for it.
"But if there was going to be time when the younger ones could stake a claim in the first team I think it could be now.
"I was disappointed (on Saturday) but I understand why I was left out.
"I don't want that to come over as expected to play but I was wishing I was.
"I can't complain. All I can hope for is that if I keep working hard, I can keep impressing the right people."