They quoted unnamed sources in Trump's transition team that is working on gearing up his new administration that will take over in January.
Trump and Vice President-elect Mike Pence are reaching out to those who were critical of them for filling positions in the new administration.
A rising star in the Republican Party, 44-year-old Haley was elected earlier on Wednesday as the vice chair of the Republican Governor's Association.
The daughter of Sikh immigrants from Amritsar, her full name is Nimrata Nikki Randhwa Haley.
She converted to Christianity when she married Michael Haley, but both she and her husband have attended gurdwara services. In 2014 both of them visited the Golden Temple in Amritsar.
If she were to get a cabinet post, she would be the first Indian American to be in the US cabinet.
It would mark a political breakthrough for Indian Americans in a year that has seen four of them elected to Congress.
Kamala Harris became the first Indian American elected to the Senate and Raja Krishnamoorthi, Pramila Jayapal and Ro Khanna won elections to the House of Representatives where they will join Ami Bera who was re-elected. The four are Democrats.
Haley's meeting with Trump and the consideration for the post of Secretary of State is a turn around for the highest ranking Indian American politician, who had publicly feuded with Trump.
She had backed Florida Governor Marc Rubio for the party's Presidential nomination and announced only last month that she would be voting for Trump, but qualified it by saying that she was not his fan.
However, on Tuesday she said, "I'm just giddy" over Trump's election, which marked a "new day".
Haley was elected Governor in 2010 and re-elected in 2014 and her current term ends in 2018.
Former US Permanent Representative to the UN, John Bolton, and former New York Mayor, Rudy Giuliani, have been mentioned as possible picks for Secretary of State.
Both of them are extremely hawkish on foreign policy, in contrast to Trump who is against foreign intervention, criticised the Iraq War and has taken a conciliatory line towards Russia.
The budding opposition to them within the Republican Party was voiced by Senator Rand Paul, who attacked Bolton for his advocacy of the Iraq War, which Trump has disavowed, and intervention in Libya.
Paul, who has an important role in the Senate Foreign Relations Committee that can block the nomination for the post, also criticised Giuliani.
Haley's public differences with Trump goes back to the Republican response to President Barack Obama's State of the Union address, which she delivered in January.
She directed criticism towards Trump over his statements about illegal immigrants, although she did not mention him by name.
"During anxious times, it can be tempting to follow the siren call of the angriest voices," she said.
"We must resist that temptation. No one who is willing to work hard, abide by our laws, and love our traditions should ever feel unwelcome in this country."
She had also said that he did not have the qualities she would want in a President.
Trump retaliated, calling her soft on illegal immigrants and that the people of her state were embarrassed by her.
But she responded gracefully with a Tweet, "Bless your heart."
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