May has scored 11 goals from 19 games so far this season and the Millers were reported to have tabled an offer last week, which was denied by J's boss Tommy Wright.
But Evans says that's not the case. "We offered £300,000 and were quoted £800,000. That price is out of our range," he told BBC Radio Sheffield.
"We left our offer on the table and asked them to get back to us and they haven't so I have to assume they value him at that amount. People in football are only worth what people are willing to pay and St Johnstone are entitled to price him up as they see fit.
"He has got a lot of attributes that I like and he's scored consistently over the last three seasons."
Meanwhile forward Tom Eaves has returned to parent club Bolton, with Evans adding: "Tom wasn't getting games and it was felt that it was best for everyone that he return.
"He has conducted himself impeccably during his time here and I wish him all the best."