The former Liverpool striker is currently sidelined with a knee injury, but Ings enjoyed a prolific start to the 2020-21 campaign with five goals and two assists in the top flight.
Furthermore, Ings notched up an impressive 22 goals in the 2019-20 Premier League season, a tally which saw him finish one behind Jamie Vardy and level with Pierre-Emerick Aubameyang in the race for the Golden Boot.
However, Ings will see his Southampton deal expire in 2022, and Hasenhuttl has called on the 28-year-old not to throw away what he has at St Mary's should a European-competing club come knocking.
Speaking to Sky Sports News, the Saints manager said: "It's normal that you get a situation like he has in a football club, and this is something special I think. I don't want him to throw this away for a few more monies.
"I speak to him once or twice a month about this topic. We must concentrate on our job here. I don't speak to him every week about his contract. It's not my job.
"It's his responsibility. He has to take the decision. Nobody else. He has to take the decision then live with the fact that he did this or that."
Ings could potentially make his Southampton return when Hasenhuttl's men make the journey across the South Coast to take on Brighton & Hove Albion on Monday evening. body check tags ::