English League One side Barnsley made an unsuccessful offer, reportedly of £100,000, for the former Scotland Under-21 player who has 18 months left on his current deal.
Ahead of the Ladbrokes Premiership clash against leaders and reigning champions Celtic at Parkhead on Wednesday night, Wright said: "I don't discuss what goes between clubs but I think reports say £100,000 and that says it all.
"But Jason is not for sale.
"We do our business the way it should be done, not in the public domain.
"It is a non-story because he is not for sale, hasn't been for sale and won't be for sale.
"We are almost there with (the new contract), there has never been any doubt that he is going to sign, he has told me that he wants to stay and he feels the best place is here to develop his game and improve and keep playing football.
"That is very pleasing but not unexpected because he is a young player who still has a lot to do, a young player who is doing extremely well at the moment.
"He fully understands the importance of playing and playing regularly."
The Perth men will face Celtic three times in their next four games – the third meeting is in the William Hill Scottish Cup – and Wright is aware the Hoops have won all 11 home league games this season.
The Northern Irishman said: "I think that says it all.
"They have been outstanding since they have come back after the winter break, they are creating a lot of chances, they are keeping clean sheets and scoring goals and they have the firepower.
"They have the resources to bring in players like (Oliver) Burke and (Timothy) Weah, so they have had a good window and they are at the top of the league because they are a really good side and favourites now to win the league.
"It is going to be an extremely difficult game and it is quite difficult to play them three times in 10 or 11 days as well but we have to deal with it and make sure we are right."