The striker scored 27 goals in his debut season in the SPFL and Wright believes May will be happy to stay at Perth after watching other promising young players such as Scott Allan and Frazer Fyvie lose their way in England.
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"It's all positive. We know that we'll have to give Stevie better terms, but we know he wants to stay. That makes it easier," said the Ulsterman. "It's harder if you have to persuade a player. Everyone talks about his playing this year, but I like how Stevie's matured as a person and dealt with all the attention. He's been excellent with the media and comes over really well.
"I've met his mum and dad twice, and Callum Davidson and Alec Cleland know them. They are sensible enough to give him the right advice. And the senior players speak to him as well. Stevie's just one of the lads here. There's no airs and graces. That's important. He wants to develop in Scotland.
"There are a few players who have gone to England, like Fraser Fyvie from Aberdeen to Wigan and Scott Allan from Dundee United to West Brom, who were good players. They're still probably good players but they've lost their way in a bigger environment. I see Scott has just been released. That's why it would be good for Stevie to stay here for at least another season."
The St Johnstone manager has already fixed up a home friendly with York City for July 19 as he builds up for the club's third successive European campaign. He is hoping to arrange a further two as the club attempt to emulate last summer's heroics over Rosenborg.
"European football will help keep the momentum going and will hopefully help season-ticket sales as well," said Wright.