Wright is mystified by reports that the Scotland under-21 cap had rejected terms to extend his stay beyond next summer.
May has been linked with an array of English clubs, including FA Cup finalists Hull City, in recent weeks. But the forward has always maintained he wants to continue his development at McDiarmid and extension talks began in the wake of the William Hill Scottish Cup final win over Dundee United last month.
"I've spoken to Stevie today and he's reiterated he wants to stay at St Johnstone," Wright said. "He wants to extend his deal here and it will be sorted. We've no idea where this story has come from. Negotiations with Stevie and his agent are ongoing and we've been going back and forward. That's the way it works and it's exactly what happened before he signed his last contract.
"Stevie's meeting with his agent over the weekend to discuss the latest offer and I don't think we're too far away."
Wright has told his players to forget about their cup success, and clear their minds for the new campaign. "As a staff and as a group of players, it's over," he insisted. "We've got to forget it and look at the challenges we have in front of us now.
"We've got a European game coming up, the players have come back in good shape and it's all about getting ready for the season ahead now."