Wright brushed off criticism from Peterborough chairman Darragh MacAnthony, who launched a rant on Twitter on Wednesday over their handling of the transfer saga.
He claimed St Johnstone wanted the fee for the Scotland U21 striker paid up front, not in instalments as the League One club prefers, but Wright says May has now ruled out a move to the League One club anyway.
Wright said: "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.
"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."