Considine was carried off on a stretcher on Thursday night after suffering a knee injury during Aberdeen' s 1-0 Europa Conference League defeat by Qarabag on a shocking pitch in Baku.
Hedges left Stark's Park on crutches last weekend after going off with a hamstring injury late on in the Premier Sports Cup defeat by Raith Rovers and the extent of his injury is also still to be properly assessed.
The Dons had an audacious bid for Hibs winger Martin Boyle rejected earlier this week and Glass will proceed on the basis of the medical updates.
"We were always looking to strengthen anyway," said Glass ahead of Sunday's cinch Premiership clash with Hearts.
"What it does is make it a bit more pressing, but the end of the window is coming up anyway. The aim was to come out the window stronger than we went in.
"If these become long-termers then that does change things a little bit but the aim is still the same, to be stronger when we come out of it."
On Considine, Glass said: "He is still sore and he will be getting assessed next week. It doesn't look great but we will wait to see the extent of the damage once he gets assessed.
"He is going to be scanned and I imagine he will need to speak to a specialist as well."
Glass has few options in central defence. Mikey Devlin is still some way off a comeback after suffering a setback in his recovery from an ankle injury.
The Dons boss stood by his comments about the pitch being to blame for Considine's injury. The 34-year-old appeared to get his studs caught in the unstable surface after being barged.
"Those comments were not coming from an emotional place, that was factual," Glass said.
"You are talking about a guy who has played close to 600 games and never done anything like that in his whole career.
"So for that to happen, from a fairly innocuous challenge, it points everything towards the pitch.
"It's a fact the pitch was a disgrace and I think their people would agree with that."