Rotherham were rebuffed following an initial approach last season but have now tried to reopen discussions following the club's promotion to the Sky Bet Championship.
Assistant manager Paul Raynor and chief scout Gee Evans were both dispatched to assess May during the Scotland Under-21s European Championship qualifier with the Netherlands on Wednesday night. The St Johnstone striker - who scored 27 goals for his club last term - was on the scoresheet in Paisley.
"I have spoken briefly with Tommy Wright [the St Johnstone manager] but I have yet to have a conversation with my chairman," said Steve Evans, the Rotherham manager.
May played a significant role for the Perth side last term and expressed a willingness to sign a contract extension following victory in the William Hill Scottish Cup final. It is a success which St Johnstone have been eager to profit from off the pitch too, with the club announcing plans to launch a new family season ticket which will allow two adults and two kids to attend matches for under £19.