Tommy Wright rules out Rangers switch
Former Rangers boss Alex McLeish is the bookmakers favourite for the job, but Wright is also said to be high up on the club's shortlist.
The Scottish giants announced the departure of Mark Warburton on Friday night after they accepted the resignation of the 54-year-old and his management team.
But Wright insists he is only concentrating on his job at St Johnstone, claiming his his success at McDiarmid Park has lead to "pure speculation".
Mark Warburton left Rangers on Friday night
The Northern Irishman said: "It is always sad to see a manager go.
"Mark had done a good job and obviously something has happened there.
"But it is all speculation. Pure speculation.
"From my point of view, for people to link me to a club that size and a club with that much history and success, and to be linked in amongst people like McLeish and other good managers, shows that I am doing a good job and the press are recognising that and linking me.
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Express Sport takes a look at some of the greatest players who have played in both the Premier League and the Scottish Premier League (now Scottish Premiership)
"In my four years as manager, we have consistently got top six so it is nice that people recognise that by linking you with the job but it is pure speculation, that's all it is and there is nothing I can do about speculation.
"My focus is really on doing the job that I am employed to do at St Johnstone. My job is to keep the level of success up in recent years.
"It gets more and more difficult every year because I do believe the league is stronger. Look how tight it is among the teams below us.
"That is my focus, to maximise what I have got at St Johnstone. That's what I try to do every day, every week, every month and every year."