The centre-half suffered a dislocated thumb as he slipped in the build up to Partick's opening goal in the 1-1 draw at McDiarmid Park on Saturday.
But the injury involved complications that required surgery and the player's surgeon has warned Wright he will not be back in action until December at the earliest.
Now the Northern Irishman has admitted holding talks with chairman Steve Brown about whether there is room in his budget to bring in a replacement.
Wright told Press Association Sport: "Steven's injury was a dislocation but the ligament in the thumb moved as well, so that made it a lot more complicated in trying to get it back in place. That is why they had to operate.
"The surgeon's report was quite negative, so we are looking at a minimum of two months. That is a massive blow for us.
"Gary Miller will get his opportunity and we also have Dave Mackay who can go in there. We're not short on quality, just numbers.
"If we can get a free agent lined up, that is something we would look at. I've spoken to the chairman about it.
"It's not something we would do ideally but we will if we think it is necessary. We are now looking around at the free agents that are out there."
Wright has already agreed a three-month deal with 21-year-old former Walsall striker George Bowerman but has been left frustrated by delays in granting him international clearance.
The Scottish Football Association is happy for the move to go through but its English counterpart is refusing to give Saints the green light to play him while it investigates a two-game stint with Conference side Woking in August after his release from Walsall.
Now Wright has called on FIFA to loosen the red tape currently tying up moves for hard-up players.
"We're still waiting on the English FA to let us know if we can play George, " said the Saints boss, who hopes to have the player in his squad for Saturday's home match with Scottish Premiership leaders Inverness.
"It would be quite harsh if he doesn't get clearance as he's just trying to earn a living.
"It was evident he was paid at Woking but we have been given assurances by his agent that he would get international clearance. We should hopefully know by Friday because it can't drag on any longer.
"We need rules but in George's situation, he's an out-of-contract professional and we're talking about denying a man a chance to earn a living, I totally disagree with that.
"Some of these rules baffle me but I don't make them up. I thought the whole idea was to allow footballers to go earn a living. But all we are doing is putting restrictions in front of them.
"Someone like George is not coming here on thousands of pounds a week. He's here because he wants to play and it's almost like expenses only. We'll only be covering his living costs.
"But he may have put himself in a position where he is caught up in a bit of red tape by playing these games for Woking.
"He only signed for five days but non-contract players are paid and he did receive payment for those five days."
- Sports & Recreation