Hull are determined to keep manager Steve Bruce and are yet to receive an approach from Southampton for his services, a source told ESPN FC.
The former Birmingham, Sunderland and Wigan boss is reportedly on Saints' shortlist to succeed Mauricio Pochettino, who left to join Tottenham last month.
But although Ronald Koeman is the favourite for the post at St Mary's, Hull are keen to keep Bruce at the KC Stadium.
The 53-year-old, who joined Hull in 2012, has one year left on his current contract and is yet to agree a new deal with City.
Bruce steered Hull to promotion in his debut year at the helm and kept them in the Premier League last season, as well as reaching the first FA Cup final in their 110-year history.
Despite losing the final 3-2 to Arsenal in extra time, the Tigers will compete in Europe for the first time next season and hope Bruce will remain in charge.
Right-back Ahmed Elmohamady, who also played for Bruce at Sunderland, praised the former Manchester United captain, who he called his "spiritual father."
The Egyptian told the Hull Daily Mail: "Steve Bruce is a great coach and I consider him to be my spiritual father.
"He brought me from ENPPI in Egypt to Sunderland and then I joined him at Hull. He means a lot to me and I credit him for what I have achieved. He believed in me and that gave me confidence.
"My love for him doesn't mean that I would follow him to any club. I am a professional player and I have my own ambitions. But it is an honour to work with a coach with the stature and capabilities of Steve Bruce."