It has been reported that the Scottish Premiership outfit want to sign the 22-year-old striker on a season-long loan deal.
According to the report, United manager Jackie McNamara has already made contact with Wednesday about recruiting the Scotland international.
United are looking for a striker this summer following the departure of Nadir Ciftci to Scottish Premiership rivals Celtic.
May joined Championship outfit Wednesday from Scottish outfit from St Johnstone in the summer of 2014.
The youngster did not have a particularly great time with the Owls during the 2014-15 campaign, as he struggled to score goals regularly.
The Scotsman could score just seven goals and managed to create just 22 chances in 39 appearances in the Championship for Wednesday last season.
May had a pass accuracy of 77% and a shot accuracy of 40%, and won 13 headers, 20 dribbles and 11 tackles.