The Saints captain has been impressive since moving to St Mary's Stadium in 2016 but his contract runs out in less than two years' time.
Southampton manager Ralph Hasenhuttl has spoken highly of Pierre-Emile Hojbjerg, saying the Saints would be happy were the captain to extend his contract at St Mary's Stadium, as reported by the Daily Echo.
The Denmark international rose through the ranks at Bundesliga giants Bayern Munich and was highly regarded by Pep Guardiola before making the move to Southampton in the summer of 2016 for a fee of £12.8million, as reported by BBC Sport.
After a slow start to life in England, the 24-year-old has gone from strength to strength for the Saints, starting 31 Premier League games last season and three this term (Transfermarkt) - and his absence from the starting XI was felt in the opening-day loss to Burnley.
With Hojbjerg's contract at Southampton - with a salary of £50,000-per-week according to Spotrac - having just under two years left to run, Hasenhuttl spoke about the captain in his pre-match press conference ahead of Saturday's Premier League trip to Sheffield United.
“We are always in contact with his agent and Pierre knows about his important role for this club," the Austrian is quoted by the Daily Echo as saying. “He is the captain of the team and is always the player I have many conversations with. His opinion is important to me also.
"He showed in the last month that he is a real captain and always positive and trying to go forward. This is what we need. Like Nathan (Redmond), it is a good signal if Pierre decides to stay with us longer. We would be happy that is for sure and he is a very important player for our team."
The Daily Echo reported that Hojbjerg was questioned about his long-term future at a recent fans' forum event that was hosted by BBC Solent, and his response, in which he claimed he was fully committed to the Saints cause but didn't want to focus on signing a new deal straight away, was seen by some supporters as a cause for concern.
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