The three-time Scotland cap is training with the William Hill Scottish Cup winners after being released by Blackburn.
But Wright is still unsure if he will be able to match the 25-year-old's wage demands while he waits for Perth chief Steven Brown to confirm his budget.
The Northern Irishman - who wants to bring in three new players - said: "David has joined us for some training.
"The club are not in a position to make him an offer now, but training here will help David out and it gives us an opportunity to get into a position to make an offer.
"It's a chance for David to do a pre-season and get a feel for the place. We can use the time David is here to sell St Johnstone to him.
"David could get a phone call and be away, but hopefully he will be here long enough for us to get something together.
"At the minute, I can't make any offers. The bottom line is we have 20 players and until I get funds we can't do anything."