May's future at Wednesday has been the subject of speculation this summer with the arrivals of Portuguese duo Marco Matias and Lucas Joao pushing him down the pecking order at Hillsborough.
May scored seven goals in all competitions for Wednesday last season and was a regular in Stuart Gray's side, but he has not been included in the matchday squad for Wednesday's opening two games of this new season.
News of May's possible availability has alerted a number of clubs, including Rangers who are keen to bring the former St Johnstone hit-man back north of the border.
Blackburn Rovers are in the market for striking reinforcements, but under their transfer embargo they are only able to sign free agents or bring in players on loan.
Rovers boss Gary Bowyer is keen to add firepower to his squad after losing Rudy Gestede and May is thought to be on his list of targets if they can bring in the Scotland international on loan.