Boss Ally McCoist has stated he would be keen for the 24-year-old, who has previously spent time with Cowdenbeath and Forfar, to go out loan again.
Gallacher will respect his manager's wishes on the matter but feels he is capable of challenging new signing Bell.
He said: "I'm more than happy here. It's a top club with top facilities.
"The gaffer wants me out on loan to get games, which is fair enough, but I really want to push here.
"It's his decision at the end of the day. It depends if I'm going to play or not and what's going to benefit me.
"I just need to train hard and, if selected, play well in the games.
"I've got my chance and I'm just thinking about doing well."
A transfer embargo means Rangers cannot register new signings - including Bell - until September 1, while competition rules state no trialists can be used in the Scottish League Cup.
As a result, Gallacher is likely to be given the nod for tomorrow's first-round tie at Forfar, having made his competitive first-team debut against Albion Rovers in the Ramsdens Cup last week.
He said: "It was an emotional moment for me because I've waited a long time to get my chance. I was delighted.
"Playing with a massive club like Rangers, there are a lot of expectations.
"But I feel as though I've progressed in the last couple of years and long may it continue."