A spate of articles in pro-government newspapers have raised the prospect of him staying on - a move that would anger his critics and require a change to the constitution.
"I am not the person who needs a third term," Kagame told a news conference when asked about speculation prompted by the articles.
"Just look at me, I don't need it. I don't do this job I am doing as a job for being paid, or as something that benefits me," he said.
Critics accuse Kagame of being authoritarian and trampling on media and political freedoms.
But he has also won international praise for progress since the 1994 genocide in his bid to transform Rwanda into a middle-income country by 2020.
The constitution currently limits presidents to two seven-year terms.
Kagame, who was re-elected with a landslide in 2010, said the constitution had been drawn up by the people and they would determine any changes to the charter. "At the end of the day, let's remember that Rwandans have to decide," he said.
One article this month in The New Times, a pro-government newspaper, reported calls by members of Kagame's Rwanda Patriotic Front for the president to stay on.
His opponents said they would oppose any attempt to change the constitution.
"We don't support the changing of the constitution. We also believe that the presidential term lengths should be reduced down to five years," Frank Habineza, president of the opposition Democratic Green Party of Rwanda, told Reuters by telephone.