Livramento was enjoying a fine debut campaign with the Saints before going down with the injury against Brighton last week.
The Englishman, signed from Chelsea last summer, was given the Terry Paine president's choice award at the club's end of season awards this week.
Asked about Livramento's status, Hasenhuttl said: "It has not happened yet, it takes a little bit, next week it will happen."
The 19-year-old is expected to miss the remainder of 2022.
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