Mikel Arteta's side have already invested heavily this window, converting Piero Hincapie's loan into a permanent deal and adding Christos Tzolis and Bruno Guimaraes for a combined £110million.
Arsenal have also been linked with Vinicius Junior and Julian Alvarez, though sources suggest both moves now appear unlikely before the deadline.
Speaking to Sky Sports, Garlick explained that Arsenal's recruitment priorities have shifted now the club is competing for major honours rather than simply building depth.
"It's players that are going to take Arsenal forward," he said.
"In the past we've looked at players that maybe helped build out the squad or get us to a certain level, but now we're competing right at the top level, and we do need to bring in players that are going to change the dial.
"That might be younger players that come into your squad and give them time to develop, and you've seen that in the last couple of years at Arsenal, and if we're able to combine those players that are coming through the academy with some of the best players in the world then we've got every chance of maintaining that success and going beyond what we've already achieved."
Garlick stressed that Arsenal's ambitions this summer go beyond simply defending last season's title and Champions League final appearance.
"We said at the start of this season we're about to embark on that we're not going to stand still and pat ourselves on the back and say, 'Well done, job done, nothing else to do'," he said. "We want to move forward - the best clubs are always moving forward.
"You can see we've already invested in the squad this season, and if the right opportunity arises, then we will look to strengthen in all areas. The window's open for the next couple of weeks, and if there are players that are going to come in and move Arsenal forward, then we will look at that."
He acknowledged, though, that finding suitable targets has become increasingly difficult given the standard the club has now set.
"The standard now is high, though - the bar's been set winning the Premier League title and getting to the Champions League final," Garlick said. "We're probably fishing in a smaller pool of quality players, and that means that it's tricky to land those players that are going to drive Arsenal forward. But if the right opportunity presents itself, we'll certainly be exploring it."
Garlick's comments echo those made previously by Arteta, who has repeatedly said he will only sanction signings that genuinely progress the squad.
"It's certainly the ambition of the club and the owners to be the best club in the world," Arteta said. "In order to do that, you need the best facilities, the best stadium, the best supporters, and you need the best squad and the best players in the world.
"Those are the ones that win you football matches and the ones that can be decisive when it matters. That's what we try to build with the actual players that we have, and with the players that we want to sign to make the difference for Arsenal."