May, who has become a target for a number of clubs after scoring 27 goals this season, has made no secret of his desire to remain at McDiarmid Park.
Speaking to Sky Sports News, Wright said: "The positive thing from the club's point of view is that he wants to stay.
"It's not like we are offering him a deal to stay, he actually wants to remain here. In any negotiations, the fact he's keen to stay at the club is a big help.
"This season has got better and better for him. He feels better playing regularly and playing in Scotland for at least another year, so hopefully we can get a deal sorted out after the cup final."
Wright, who won the Irish League Cup while in charge of Distillery in 2011, believes the experience gained with the Lisburn club will aid his preparations ahead of this weekend's final at Celtic Park.
"It will help in terms of preparation and build-up to the match, although in Scotland it has been a lot more intense with more media commitments.
"We were 1-0 down in that final but weren't afraid to make changes and we went on to win. So that will give me a little insight into what I can expect on Saturday."
Watch St Johnstone take on Dundee United live from Celtic Park from 2.30pm this Saturday on Sky Sports 1