Ms Gray left as the PM's chief of staff after just three months in the role, following weeks of negative headlines and briefings against her, including a row over her salary.
She was replaced by Morgan McSweeney, with whom she had reportedly clashed in his previous role as Sir Keir's chief political adviser.
Downing Street had previously said the envoy role would be "vital" in "strengthening our relations with the regions and nations".
However, it had not published details of Ms Gray's new responsibilities, and last month she did not attend the first-ever meeting of a new Council of Nations and Regions.
At the time, the government said she was taking a short break before starting her new role, but did not specify how long for.
Now her allies have confirmed she will not be taking up the role.
"She's taken time to think about it properly, talking to stakeholders, but ultimately she's decided she doesn't want to do it," a friend said.
Ms Gray, who became a household name after leading the government's internal inquiry into the Partygate scandal, left the civil service to become a senior adviser to Sir Keir last year.