The 54-year-old Welshman, who was sacked by Stoke in January, was brought in on a short-term deal in March after Mauricio Pellegrino was axed with the Saints struggling in their battle to avoid relegation.
And, after guiding the Saints to safety courtesy of two wins and two draws in eight games including last week’s vital 1-0 victory at relegation rivals Swansea, the St Mary’s outfit are keen to keep him on board for the foreseeable future.
‘We began conversations after the Swansea game and they continue this week and they are good conversations,’ Krueger told Sky Sports.
‘He came in with his group and they just fit like a glove. They embraced the Southampton culture and our values and they felt aligned immediately and they were just part of the fabric within 10 days – it was crazy.
‘Hopefully we can come together and grow with this.’
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