Sousa's name has been mentioned as being amongst the candidates being considered by The Clarets as a replacement for Owen Coyle, who is set to take on the managers job at Bolton.
However, Swans chairman Huw Jenkins has said that should Burnley ask permission to talk with Sousa they will be denied.
"If a manager is relatively successful with a club in the Championship, he is always going to be mentioned when a vacancy comes up in the Premier League," Jenkins told the South Wales Evening Post.
"But I would say two things:
"One, I don't think Burnley will be getting in touch with me.
And two, even if they do, I think you can state that I won't be letting any club talk to our manager.
"I think the biggest thing this shows is that we have a steady, stable football club which is well run.
"We give every manager an opportunity to succeed if they have talent, and Paulo has shown he has talent.
"He had a difficult task following Roberto and we all know about the injury problems he had to cope with at the start of the season, but we have come through that as a club now.
"Swansea City give any manager a good platform to work from these days, that's why Paulo wanted the job, and I think most people within the game now recognise that."
Source: Team Talk