Millers boss Steve Evans this week publicly claimed he had a £300,000 bid rejected and was told that Saints valued the 21-year-old at around £800,000.
But Wright, who has denied any bid has been made on two occasions, said to the Scottish press: "We haven't quoted any figures and we won't be quoting any figures. We know our valuation of the player and if and when that's met, and it suits Stevie as well, that's when something will happen.
"But I'm not going to be putting figures on Stevie's head in the public domain. I don't think it's fair on the player."
St Johnstone played down reports of Rotherham's interest after it was leaked, before Evans gave his public take on negotiations.
"That's two dealings we have had with English clubs and they seem to want to ruffle a few feathers," added Wright.
May's proposed move to Peterborough had broken down in August after a row broke out between the Scottish side and Posh officials over fee installments, with the transfer eventually falling through.