The Northern Irishman believes the 25-year-old former Kilmarnock and Cardiff player, who had a loan spell at Hibernian among others, is probably close to agreeing a pre-contract with Aberdeen.
However, Hearts have notified the McDiarmid Park club that they also plan to talk to Kennedy.
Wright told Saints TV: "The situation is quite simple. It is his right to talk to other clubs. He is in the last six months of his contract.
"Aberdeen contacted us officially, Hearts made contact yesterday and they plan to speak to him.
"Aberdeen, I think are probably close to agreeing a pre-contract with him and I want him to stay.
"So there is basically three scenarios as I see at the minute.
"One that I want to happen is that he stays to the end of the season and I can't see that being a problem.
"The other scenario is he goes to Hearts and the other scenario is he goes to Aberdeen, but for that to happen obviously we are going to need something the other way.
"I don't think at this stage it is in our interest to allow him to go. He is an important player for us.
"I don't see a problem with him staying. Whether he signs a pre-contract or not, I am hoping he is going to be here until the end of the season."
Wright confirmed he is interested in Inverness right-back Shaun Rooney on a pre-contract agreement.
The Northern Irishman said: "Like all clubs we are planning for the summer.
"We do things right and sometimes it can be to your detriment but we play to the rules.
"We have emailed certain clubs about certain players and we plan to speak to them in terms of pre-contracts.
"That particular player, we have made Inverness aware. I have spoken to (Caley boss) John Robertson about it as well.
"That will be something that we are looking to do.
"We want to bring people in during this window as well but that can't happen until we get people out."