Sousa has only been in the Liberty Stadium job since last summer, filling the void created by Roberto Martinez's exit to Wigan, but has done a sterling job during his short time at the helm.
He has the Swans well-placed to launch a New Year promotion push in the Championship and the Welsh outfit are understandably reluctant to see their highly-rated coach tread a similar path as his predecessor and defect to the Premier League.
"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," Swansea chairman Huw 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."
While keen to fend off the reported interest in Sousa's services, Jenkins believes speculation regarding their manager should be regarded as a complement.
"I think the biggest thing this shows is that we have a steady, stable football club which is well run," he added.
"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."
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