Wright has emerged as United's top candidate after leading Saints to the 2014 William Hill Scottish Cup and three consecutive top-six finishes.
But St Johnstone chairman Steve Brown has declared that he is not interested in striking a compensation deal with their Tayside rivals.
In a statement on the club's official website, Brown said: "The manager has never indicated that he wishes to leave the club and I have spoken with Tommy regarding this particular matter and he has reiterated to me that he is more than happy at Saints.
"Since I appointed Tommy, I have had a good working relationship with him and we are both striving to maintain the success we have enjoyed in recent seasons and therefore, regardless of any approach and any level of compensation that might be offered, it will be flatly turned down.
"It is important to me that all St Johnstone supporters are assured that we intend for Tommy to remain at the club beyond his current contract which already runs to June 2017."