May had stated he was prepared to sign a new contract with the Perth club this summer but that did not happen and his existing deal is due to run out at the end of this season.
That could make a seven-figure offer irresistible to St Johnstone, although a move would also depend on whether May himself was prepared to join the English club which was promoted in May via the League 1 play-offs. St Johnstone have allowed another striker, Nigel Hasselbaink, to leave this summer already, with the Dutchman having since signed a two-year contract with Greek Super League side FC Veria.
Steve Evans, the Rotherham manager, has attempted to sign May before but previous attempts were rebuffed by Steve Brown, the St Johnstone chairman. However, last night the Perth club confirmed that talks were ongoing. The 21-year-old scored 27 times last season and became an iconic figure in their triumphant run in the William Hill Scottish Cup.
It is believed that Rotherham may be prepared to pay £600,000 up front and the remainder in instalments over the coming season. The club reportedly broke its transfer record to sign Jordan Bowery from Aston Villa last month, although the fee was undisclosed, but the sum on offer for May would take their club record even higher.
A club statement last night read: "St Johnstone can confirm that they have received an approach from Rotherham United regarding Stevie May and talks between the two clubs are ongoing."