The Posh have so far failed to match the Perth club's valuation of the player but have yet to drop their interest.
If May does seal his departure from Saints, Wright is confident of beating the transfer deadline to fill the void left by the 20-year-old.
He said: "We've got a few irons in the fire that we could possibly look at. A lot would depend on if and when Stevie goes and any fee we would get.
"There are still a lot of players out of work so there will be options."
There had been suggestions that Peterborough had ended their interest in May but Wright confirmed talks remain ongoing.
He added: "I think there was a tweet from their chairman saying they were no longer interested. Then we got a phonecall the next day so it's still ongoing. It's back with them at the minute and there's nothing more to report on it really. It's not dead in the water yet."
St Johnstone play host to Ross County in the Scottish Premiership on Saturday and Wright insists his players are now well over their Europa League disappointment.
Saints crashed out of the third qualifying round on penalties to Minsk last Thursday, before taking a point from a goalless draw at Kilmarnock on Sunday.
Wright said: "It's well over a week now and we have trained well this week. I think it was more the physical exertions that they had to put in on the Thursday night which may have led to a poorer performance on Sunday in terms of possession.
"But I'm taking nothing away from Kilmarnock, they played really well on the day. I've no doubts that the players are over their disappointment."
He added: "It will be a tough game tomorrow. Ross County will be looking for their first points, which gives them plenty of motivation.
"We are looking to build on what's been a good start for us; a win at home and a draw away from home. I don't think there are any easy games in the top-flight and tomorrow will be no different."
Saints will be without first-choice goalkeeper Alan Mannus, who has been ruled out of action for up to six weeks with a shoulder injury. He will be replaced between the sticks by back-up keeper/goalkeeping coach Steve Banks.
Wright said: "It's disappointing for Alan but it's just something we have to get on with, there's not a lot we can do about it. Steve Banks will come in and he's got a lot of experience so there are no problems in that department."