The twenty second amendment, which was added to the constitution in 1951 after President Franklin D Roosevelt was elected four times in a row, says: "no person shall be elected to the office of the President more than twice".
But Trump on Sunday suggested that was a minor detail.
"There are methods which you could do it," Trump told NBC News.
He also said: "It is far too early to think about it".
Asked if one potential avenue to a third term was having Vice President JD Vance run for the top job and then pass the baton to him, Trump said: "Well, that's one. But there are others too".
He then refused to elaborate.
Changing the US constitution to dump the two term limit would be difficult, political experts say.
Vance's office did not immediately respond to a request for comment from The Associated Press.
Trump, who would be 82 at the end of his second term, was asked whether he would want to keep serving in "the toughest job in the country" at that point.
"Well, I like working," the president said.
He suggested that Americans would go along with a third term because of his popularity.
He falsely claimed to have "the highest poll numbers of any Republican for the last 100 years".
Gallup data shows President George W Bush reaching a 90 per cent approval rating after the attacks on Sept. 11, 2001.
His father, President George H.W. Bush, hit 89 per cent following the Gulf War in 1991.
Trump has maxed out at 47 per cent in Gallup data during his second term, despite claiming to be "in the high 70s in many polls, in the real polls".
Trump has mused before about serving longer than two terms before, generally with jokes to friendly audiences.
"Am I allowed to run again?" he said during a House Republican retreat in January.
