The 26-goal frontman has been linked with moves to Rotherham, Peterborough and Preston this season after firing Saints into the Scottish Premiership top six and the final of the William Hill Scottish Cup.
But McDiarmid boss Tommy Wright has not given up hope of tying the 21-year-old down on a fresh deal and will meet with May and his representatives in the coming days to discuss the possibility of a new contract.
The PFA Scotland young player of the year award nominee told Press Association Sport: "We're hoping to sit down in the next week or so, have a discussion and see what both parties have got to say.
"I don't see any reason why I shouldn't be here next season. I love it here and I've had a successful season.
"It's a club that is close to my heart. I live just round the corner from the stadium, which is perfect for me and my family.
"There is no reason for me to say I want away. I'm in no rush to move to England. I'm still improving and this is the perfect club for me to develop at."
Scotland boss Gordon Strachan is considering handing the Under-21 striker a full call-up ahead of the May 28 friendly with Nigeria in London.
And May says that would cap off the best season of his fledgling career.
Saints' top-scorer - who returned to Perth this season after spending the previous 18 months on loan at lower-league outfits Alloa and Hamilton - said: "I heard what Gordon said and if I got a call-up it would be the perfect end to a perfect season.
"I believe I'm ready for international football. It is a big step up but if I was fortunate enough to get that chance I'd be honoured to represent my country.
"We've got the cup final coming up so it could be a fantastic couple of weeks if it does come true.
"It's hard to believe I was playing in the Third Division with Alloa only a couple of seasons ago and now I might get a chance with Scotland. Andy Robertson has done that already after moving from Queen's Park to Dundee United but it only took him one season."
St Johnstone face Aberdeen on Saturday just a fortnight after ending the League Cup winners' hopes of a trophy double.
May netted twice in their 2-1 Scottish Cup semi-final as he silenced the Dons' support, who had mocked the striker every time he has come up against their side this term.
But it was May who had the last laugh after sending Saints into their first ever Scottish Cup final.
"I don't think I'll get quite so much stick this time," he said. "They won't be singing that song quite so much. But it is all just banter and I can take it.
"Saturday's game will be a bit tasty because of what happened in the semi-final but we're looking forward to it."