According to the Daily Record, the Dons have already approached Sheffield Wednesday manager Stuart Gray regarding the transfer.
May, 22, only arrived at Hillsborough from Perth last summer, but he has reportedly struggled to settle in England.
The hot-shot scored 27 goals in 49 games in his last season with the Saints, taking them to Scottish Cup glory, but he only hit nine for the Owls last term.
And with Wednesday keen on securing a prolific goalscorer, the Dons could scoop up May on a season-long loan deal as they look to mount a serious title challenge and progress in Europe.