Spurs have been in the market for another forward to help spell Harry Kane, and the Saints man appeared on their radar in recent weeks after a stunning 2019-20 season.
Ings narrowly missed out on the Premier League Golden Boot by scoring 22 goals last term, earning a recall to the England national team in the process.
Though the 28-year-old's form has seen him linked with a move away, Hasenhuttl said that Ings has no interest in leaving the club.
"The only thing I want to say for these rumours is that there is absolutely zero interest from Danny to go anywhere," Hasenhuttl said at his press conference on Friday. "He is 100 per cent happy here. For us it is not discussable. He loves what we do here and he loves to play for us."
Jose Mourinho and Spurs will have the chance to see what they are missing on Sunday when they visit St. Mary's to take on Ings and Southampton.
Elsewhere on Friday, Tottenham appeared to miss out on another striker target when Trabzonspor confirmed their star forward Alexander Sorloth would be joining RB Leipzig.
Trabzonspor president Ahmet Agaoglu confirmed that his side had reached an agreement with RB Leipzig for Sorloth, who finished the 2019-20 season with a total of 33 goals in all competitions.
Sorloth was in the middle of a two-season loan at Trabzonspor from Crystal Palace, meaning discussions on his sale had to take place between three clubs.
"Within the framework of an agreement that is unique in Turkish football history, the player will be transferred to the Leipzig club," Agaoglu said.
Agaoglu confirmed on Sunday that Tottenham had joined the chase for Sorloth's signature, telling Fanatik: "We are meeting with Leipzig and Tottenham, ourselves and Crystal Palace."
Tottenham will be back in action on Sunday at St. Mary's after a disappointing start to their season last weekend. Mourinho's men lost 1-0 at home to Everton, after which the Portuguese boss called out some of his players as "lazy."