Ms Goodwin said Mr Korski – then a special adviser at No 10 – had put his hand on her breast during a meeting at Downing Street in 2013.
She said she had not previously reported the incident because of attitudes at the time.
However, she said she made a formal complaint to the Cabinet Office on Tuesday.
She told the Times a senior official had told her the options were either to refer the incident to the police or to do nothing because Mr Korski no longer worked in Downing Street.
Conservative MP Caroline Nokes, who chairs the Commons women and equalities committee, has said the way sexual harassment complaints in Parliament are dealt with is too slow and “opaque”.
Ms Goodwin, who was behind the successful ITV drama Victoria, wrote about the alleged incident in 2017 but did not name Mr Korski until Monday, saying she hoped this would encourage other women to come forward.
She said that since the article’s publication other women had contacted her with “interesting stories”, but added she could not provide details for legal reasons.
Two days later Mr Korski said he was withdrawing from the mayoral contest because the pressure on his family and the “inability to get a hearing” for his message “makes it impossible for my campaign to carry on”.
He continues to deny the allegation and said he would welcome any investigation.
A Cabinet Office spokesperson said: “The Cabinet Office has been approached by an individual in relation to this matter and they have been directed to the relevant authorities for such allegations.”
Mr Korski was one of three candidates shortlisted by the Conservative Party ahead of next year’s election, when Labour’s Sadiq Khan will be running for a third term as mayor.
It leaves London Assembly member Susan Hall and barrister Moz Hossain as the two remaining contenders to be the Conservative mayoral candidate.
But the Conservatives said the race would continue with the two remaining candidates.
Who is Daniel Korski?
Born in Denmark and the son of Polish emigres, Mr Korski was deputy head of the Number 10 policy unit between 2013 and 2016.
A campaigner to stay in the EU, he left Number 10 when David Cameron did after the Brexit referendum. He has previously worked for a think tank and as a journalist.
He is a technology entrepreneur, having set up his own business providing support for companies seeking contracts in the public sector.
The central message of his campaign to be the Conservatives’ mayoral candidate was enabling people to achieve the “London dream”.
His key offer was the pledge to provide new solutions to old problems, such as pay-per-mile road-pricing to tackle congestion and air pollution in the capital.