The former St Johnstone striker will line up for Billy Stark's side in a European Championship qualifier in Slovakia and against Luxembourg on Monday and will be too old for the next campaign.
May has already made an impact at Hillsborough since his £800,000 move from Perth last month and netted his first goal for the club at Middlesbrough. He was tipped for a full Scotland call-up and manager Gordon Strachan admitted last term he was tempted to summon him for the end-of-season friendly in London against Nigeria. The 21-year-old is now concentrating on grabbing a couple of wins for his country against the Slovaks and Luxembourg that would propel Stark's side up to second place with a very slim outside chance of reaching the play-offs.
May said: "It would be nice to bow out on a high. We know these two games are going to be tough, but we will treat them with respect.
"Of course, anyone would say if you had the preference you would rather be with the full national squad, but I'm happy here and these games are qualifiers, which are nice to play in and they do matter as opposed to friendlies.
"There are pros and cons, but I'm not thinking too much about the getting called up versus not getting called up thing. There are a lot of top international strikers in the full squad so I can't be disappointed.
"Playing at the highest level possible is a personal goal for me. That's what I went down there to do. If that comes with an international call-up down the line then good.
"The boys at Sheffield Wednesday have all been great with me and welcoming as a club. It's a hard league to play in but I'm enjoying the task of that. I'm coping relatively well."
May has already noted a big difference between the English Championship and the Scottish Premiership - the playing surfaces.
He said: "It is a high standard. The pitches are a big thing to do with it. The surfaces down there, you can trust your touch much more with the flat grass which you don't really get as much of in Scotland as you would like. And if the pitches were at that standard you would see the standard in Scotland going up that little bit more. It's probably easier said that done to get these kind of pitches. It's not cheap to get pitches like that in and look after them to the standards they do down there."