May has netted 27 goals in all competitions this season and is sure to again be a target for clubs south of the border this summer but his Saints mate Millar believes the interest should be coming from teams in England's top flight.
"If Stevie decided he wanted to try down south then nobody could fault him for that," he said.
"But I don't think the clubs who have been linked with Stevie would be right for him and I don't mean any disrespect.
"If he's in the Scottish Premiership he's involved in big games against Celtic, we're looking forward to the Cup Final and then there's Europe - is that not where you want to develop?
"Going down to League One or League Two isn't for him on his current form. You're looking at Championship or even top flight in England because he has proved he can score at every level.
"If he goes on to score 30 goals it would be massive. Guys such as Henrik Larsson and Kris Boyd scored 30 goals for teams who are dominant in almost every game."
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