The Dane joined Haas in 2017, a year after the team made its grand prix debut, staying there until he lost his drive at the end of the 2020 season.
Magnussen made a surprise return to Haas for 2022 after the team ousted Nikita Mazepin and Russian title sponsor Uralkali over the invasion of Ukraine.
Magnussen's current contract expires at the end of this year, but the 31-year-old wants to extend his stay to fulfil the untapped potential he believes the team has.
"I think I still feel like there's so much unfinished business here," said Magnussen. "I feel like it's always been. I've been here for many years now. There's always been some potential that we haven't seemed to really exploit.
"And I feel like now we are building a better foundation to go and exploit that potential. I feel we have some very talented people in the house. And I think we've had that since day one.
"You know, many people didn't give us a lot of credit in the beginning, because they thought we were just copying Ferrari, but we've shown quite a few times that we don't just copy, we are doing our thing.
"And I think this year, we're copying someone else other than Ferrari. We are copying Red Bull, so is everyone else. think there's a lot of talent here and I think there's some potential that that I'd like to see fulfilled.
He added: "I'm like everyone else, focusing on this year and at the same time open to any opportunity. So as I said, I just told you how I feel about the opportunity of staying at Haas, I think that is naturally the most likely option."
Asked if he had already started talks to renew his contract, Magnussen said: "Not like concrete. When you're part of the team, you're talking all the time, I think there's much focus on the season and things."
Should Magnussen stay at Haas for another year, the Danish driver will have a different team-mate after Nico Hulkenberg decided to sign with Sauber for 2025 ahead of Audi's entry.
Magnussen admitted the German's move came as a surprise to him.
"Honestly, I thought it would be me and Nico again next year. I thought that would be likely," Magnussen added.
"Obviously, he has taken the opportunity with Sauber and Audi. I wish him all the best with that. We will continue focusing and enjoying this year. Continuing the progress that we've made as a team for this year, and hopefully building on that beyond this year as well.
"I actually feel like we are working quite well as a team. It's competitive, but it's helped me. It's not like we're getting in each other's way. It can be very unhealthy in F1 sometimes, and we're two very grown-up drivers and quite sensible. Both.
"Hopefully if I continue with the team and it's going to be a new team-mate, hopefully it will be as good with the next guy."
A troubled Miami GP left Magnussen just two points away from a race ban as he now accumulates 10 penalty points on his licence.
