Senior Republican senator Marco Rubio from Florida was questioned on Sunday over the possibility of a primary challenge by Ivanka in 2022. Fox News host Chris Wallace asked: “How seriously do you take Ivanka Trump as a potential opponent?”
Mr Rubio responded: “Well, I, I, I don’t really get into the parlour games of Washington.
“When you decide to run for re-election in a state like Florida, you have to be prepared for a competitive race, you run it like a competitive race, so that’s what I’m preparing to run, a very competitive race against a tough opponent.
“I don’t own the Senate seat, it doesn’t belong to me. If I want to be back in the US Senate I have to earn that every six years.”
It follows speculation about Ivanka’s future career in US politics after she and husband Jared Kushner purchased a property in Miami.
According to The Wall Street Journal, the former First Daughter Ivanka and her husband have signed a deal to lease a condominium in Arte, Florida.
A source told the paper the couple signed a deal to lease a large, unfurnished unit in the development for at least a year.
The deal is thought to be temporary while Ivanka and Jared build a house on a lot they purchased on Miami’s Indian Creek Island for $32 million (£23 million).
During his interview on Fox News, Mr Rubio said: “I like Ivanka, and we worked very well together on issues.”
Other Twitter users claimed Ivanka will “primary Marco Rubio” in 2022.
One user posted: “Someone tell Marco Rubio it doesn’t matter what he says. Ivanka will still primary him.”
In 2017, a photograph of Mr Rubio trying to hug Ms Trump in Washington went viral.
The Florida senator appeared to fail in an attempt to hug the former First Daughter.
During Donald Trump’s four years in the White House, Ivanka served as Advisor to the President and the Director of Office of Economic Initiatives and Entrepreneurship.
Mr Trump has repeatedly touted his daughter as capable of being the first female US President.
But Kate Bennett, CNN White House correspondent, says sources revealed Ivanka to be “in a bit of a panic” about her future.
She said: “I talked to a lot of sources today who say they’re questioning everything now, from where they’re going to live after the White House to what their careers will be.”