Lara, a former television producer and personal trainer, is married to Eric Trump, 36, the president's second eldest son.
Eric Trump, left, son of President Donald Trump and wife Lara Trump depart after a news conference on legal challenges to vote counting in Pennsylvania. Photo / AP
She told Fox News: "It would be an incredible thing. It's my home state, a state I love so much. And look, I think we need some strong Republicans in Washington DC.
"We had a great run with the Senate and the House this go round, but you know, let's see what happens. Let's get through this one and then we'll talk about the next one."
During the last campaign Lara spoke at events and rallies around the country, including many in North Carolina, and had her own YouTube show. She backed her father-in-law's claims about voter fraud.
Each state sends two senators to Washington and the next Senate election in North Carolina takes place in 2022.
The Republican incumbent, Richard Burr, plans to stand down, which could lead to numerous candidates entering the party's primary race.
Mark Meadows, Trump's chief of staff, is also from North Carolina. But Meadows said: In terms of my hat, it won't be in the ring."
Donald Trump narrowly won North Carolina, by 1.3 per cent, in the 2020 election.
Ivanka Trump, 39, the president's daughter, and adviser, has not indicated any plans to run for public office in the immediate future.
She is reportedly still deciding whether to move her family from Washington to New York, New Jersey or Florida.
At the president's golf resort in Bedminster, New Jersey the "cottage" used by Ms Trump and her husband Jared Kushner has, for some time, been undergoing renovations including extra bedrooms and a veranda.
It has led to speculation they may move there. However, the couple have kept their spacious former apartment in Manhattan.
They are reportedly considering spending more time in both New Jersey and Florida, where Trump is expected to be based after his presidency.
