According to the New York Times, Ivanka Trump's name was once floated for the UN Ambassador position.

The New York Times on Saturday published a piece detailing how White House senior adviser Jared Kushner's role has shrunk after John Kelly joined as chief of staff.

The article also delves into some of the political challenges Kushner and Ivanka Trump have faced in Washington, D.C., and some of their friends have indicated that they may be looking to return to New York.
"At one point this fall, a scenario circulated in which Ms. Trump could replace Nikki R. Haley as ambassador to the United Nations if Ms. Haley replaced Secretary of State Rex W. Tillerson," notes the Times.
While there was speculation weeks ago that Haley might take over Tillerson's role, she rejected that possibility, telling CNN in October, "I would not take it...I want to be where I'm most effective."
President Trump has expressed doubt about Tillerson's future amid reported tensions between the two men.
In an early November interview on Fox News' 'The Ingraham Angle,' he responded "we will see" to a question about whether Tillerson will remain in his post for the duration of the term. 
Trump also gave a lukewarm assessment of the secretary's job performance, commenting, "Rex is in there working hard. He's doing his best, he's doing the best he can."
However, at this time, a high-level diplomatic shake-up seems unlikely, at least in the very near term.
The Times adds about Ivanka and the UN Ambassador role, "Aides to Mr. Trump said they never heard that discussed internally, and the latest betting now has Ms. Haley staying put."