The ex-civil servant was said to be on a short break before taking up her new post.
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However, reports on Tuesday said this was now no longer happening.
There was some confusion over whether Ms Gray had declined to take the role or if the Prime Minister had withdrawn the job offer.
Early in the day, the Guido Fawkes blog quoted a Downing Street source who said she was now “very unlikely” to do the role, as “not least as no one can work out what it is.”
They also pointed to comments made by John Swinney, who told Newsnight he “won’t be dealing through envoys.”
Allies of Ms Gray told the FT that she had walked away.
“Sue has taken a decision not to take the role. She’s going to focus on other things,” one said.
The person added: “She’s taken time to think about it properly, talking to stakeholders, but ultimately she’s decided she doesn’t want to do it.
Downing Street had previously described her new role as a “vital role in strengthening our relations with the regions and nations”.
