The rumours said the German could be set to switch to another team, or simply sit out the rest of the 2013 season before making his next move, after not being paid in recent months.
The rumours said Hulkenberg's move could be good news for Sauber reserve Robin Frijns, who has just lost his GP2 drive due to a lack of sponsorship.
But Hulkenberg on Thursday said talk he is about to leave Sauber is "rubbish".
Asked in Hungary if he is staying put at the Swiss team for the rest of 2013, he told British broadcaster Sky: "Absolutely."
Beyond this year, however, Hulkenberg admitted the future is "open".
"My management and I are looking at all the possible options, including Sauber," he said.