"The option that Renault has on me was extended by two weeks but it's run out. I'm a free agent," Magnussen told Reuters after qualifying at the U.S. Grand Prix on Saturday.
"I'm very hopeful I can stay with this team. I think they are one of the teams that can fight for world championships in the future...but only time will tell."
Magnussen or British team mate Jolyon Palmer, or possibly both, will leave at the end of the season after Renault last week announced Germany's Hulkenberg was joining from Force India.
The second seat is the only one still open at a manufacturer-owned team and there are a number of potential candidates including Manor Racing's 20-year-old French rookie Esteban Ocon.
Finnish driver Valtteri Bottas has also been mentioned in speculation although he is expected to stay at Williams.
Palmer, whose performances have improved and who out-qualified Magnussen on Saturday, is also out of contract at the end of the season.
"I'm just trying to do the best I can to take the second seat," he told Reuters. "I think the fact it's still open means they haven't decided which means everything I can do is good.
"I really feel like I'm getting the most out of what I've got now," he added.
"I think me and Kevin have overall done a good job for the team and got on really well with the team and worked hard for it but obviously one of us is gone."
Palmer said the vacancy at Force India was also an attractive option that he would be open to.
"As far as the other ones (team vacancies) go, we'll see what's on the table after that," he added.
Renault team principal Frederic Vasseur, who worked with Hulkenberg in the junior series, said the British-based team would take their time to decide the line-up.
"We are in talks with many drivers. For sure (the fact) we have secured the situation with Nico buys us time. Now we can postpone the decision for the second cockpit," he told the official Formula1.com website.
"Yes, we do have some young drivers and rookies in the loop so it is important to see how they are improving."
(Editing by Tony Jimenez)
