The Demons have met with May and have joined Collingwood, Hawthorn and Essendon as the clubs vying for the key defenders signature.
Melbourne’s current key defenders Oscar McDonald and Sam Frost have excelled this season, but there are still questions over their ability to play on the powerful key forwards.
While the Demons are interested in May, they will have difficulty trading for the Gold Coast star.
The Demons have made room in their salary cap to lure a big-name player in the trade period, but do not have a first-round draft pick this year, which reduces their chances of agreeing a deal with the Suns.
The Demons situation would change if Jesse Hogan decided he wanted to leave the club. Hogan spoke to Fremantle last year and has always been rumoured to return to Perth to be with his family.
Hogan has indicated he is happy at the Demons and still has two years to run on his current contract.
But the Demons may want to offload the 23-year-old after the emergence of Sam Weideman in this year’s finals series.
The Suns will play hard ball for May if he seeks a trade. The captain has a year left on his contract, before becoming a free agent next season. If he exercised his free agency rights, the Suns would receive a first round selection, which could be higher than what any of the interested clubs could offer this season.