Saints have lost eight of their last 11 league games, winning only one of those fixtures.
The Sun says Saints remain committed to the Austrian, who has been in charge since December 2018.
It is believed that some internal discussions amongst the club's hierarchy were had about Hasenhuttl's position.
But the conclusion was the 54-year-old continues to be fundamental to their project and he will be in charge next season to execute it.
There is a feeling though that improvements need to be made and some changes need to happen this summer.
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