The club confirmed on Thursday that Houston will leave Tannadice when his contract expires in the summer.
The 54-year-old had been in talks over a new deal but opted against remaining on Tayside on reduced terms. He cited more cutbacks at the club, combined with his desire to progress as a manager, as the motivating factors behind his planned departure.
However, Thompson believes there will be no shortage of interested parties in the post, and he said: "I think a number of people will be interested in the job. We've got a great fan base, we're a great club and we've got fantastic training facilities at St Andrews.
"With our record over the last few years, I think it would be a club that people would want to come to."
Former St Johnstone boss Derek McInnes has already been linked with the job, having recently parted company with Bristol City.
Thompson added: "We haven't got anyone in mind. It gives the board time to look at things. Whether we find somebody in four weeks, two months or three months, time will tell.
"Normally, in football, the manager goes on the Monday and they're looking to get the new manager in on the Wednesday, which makes it extremely difficult.
"We've been there and you don't always get a chance to think properly and clearly when you're doing that.
"What we do have here is a position where we can sit down and say: 'What are we looking for at the club? Who are we looking for as a manager?' I think it makes it a bit easier for us."
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