The 26-goal striker has been linked with League One trio Rotherham, Peterborough and Preston after another impressive season, including a brace against Aberdeen this month which took St Johnstone to their first Scottish Cup final.
May said: "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'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 understood to be considering handing the U21 striker a full call-up for the friendly with Nigeria at Craven Cottage on 28 May.
"If I got the call it would be the perfect end to a perfect season," he said.
"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."