The 20-year old striker has been the subject of interest from the Posh with the League One club’s chairman Darragh MacAnthony criticising the Saints on Twitter for the way they had handled the transfer dealings.
But Wright brushed off the words from MacAnthony, saying that May would not be departing McDiarmid Park anytime soon and certainly not to join Peterborough.
"We tend to do our talking through proper media channels. We don't need to be going into social media, I don't think that's the right way to do it,” said Wright.
"Some of the things he says could be quite easily contradicted but he can rant and say all he wants, Stevie May won't be going to Peterborough.
"I had a short conversation with Stevie yesterday and he told me he wouldn't be going to Peterborough so maybe that's why their rant came about.
"But I have a football club to run and he's got a Twitter account to run so we'll just leave it at that."