The prolific centre-forward has scored 38 goals in 75 games for the Saints.
He could be back in the team against Brighton on Monday night after a spell out with a knee injury.
Asking about the future of Ings, whose contract expires in 2022, Hasenhuttl believes it is firmly with the Saints.
He told reporters, via the Daily Echo: "Yes, the decision is clear - that he stays with us until the end of his contract.
"Either (that or) there comes a club that pays the money we want to have for him and then he can leave, but I don't know if he wants this, I don't know if he wants to leave.
"I know what he has with the club. I know how much the fans love him here and what we can give him.
"I mean, he made it as an English international from this club, so you don't have to be part of a top six club to reach the internationals for England. So also this we could manage for him.
"I mean, there are some reasons. Yeah, sure, money is always a good argument, especially when you look at the bigger clubs, how much they can spend on players. But I think we wanted to show him how much we want him.
"Definitely I think this message is coming and the rest is on him to decide if he wants to stay with us.
"If not, we will also find a future. But I hope he will, because he's a very important player for our team.
"We do everything (so) that he can score for the team. The team works for him and he works for the team, so it's a good relationship.
"For me it's a very important signal that I see that more and more players want to sign here and more and more players want to stay with us. And the rest is up to him."
Hasenhuttl added: "If he doesn't want to sign a new contract, then he stays with us, and I only sell him if there is an offer that we definitely cannot deny.
"But he is not 20 or 22 years old. And I think a top club, yes, has an alternative to take him.
"I think this is not what he wants to do and the rest we can also offer him. So I am still positive that he stays with us and I don't think about anything else. He knows how much we want him.
"I think he feels comfortable. He feels the atmosphere is fantastic to play good football. He enjoys playing with us. I don't see any reason why he shouldn't stay with us."
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