The Labour mayor announced he will host a business summit in the new year which will consider proposals, floated by the London Chamber of Commerce and City of London Corporation, for special work permits to allow EU nationals to take up jobs in the city.
Speaking to the Institute of Directors on Wednesday evening, Mr Khan is expected to say he is pressing the Government to adopt a negotiating stance which satisfies businesses' demands for skilled workers.
But he will tell business leaders that his monthly meetings with Brexit Secretary David Davis have given him the impression that "it doesn't look like they are listening".
Khan will say: "London's businesses must retain access to the skilled workforce they need in order to grow - it's absolutely essential to protecting jobs, growth and tax revenues across Britain over the next decade.
"I will keep pushing the Government to recognise this vital need in their negotiating position - but it doesn't look like they are listening.
"If the Government ignores the needs of business and pushes ahead with a new system that cuts off access to skilled workers, then we will have no choice but to look at a London-specific solution."
Setting out plans for a London summit, he will add: "The City of London Corporation and London Chamber of Commerce have already done some crucial early thinking about options - but we need to go further and faster to make the case to the Government and develop a new system.
"I will bring together industry leaders, business representatives and experts at City Hall in the new year to take this vital work forward."
Around 616,000 people born elsewhere in Europe work in London, making up 12.5% of the capital's workforce. They include 88,000 in the construction industry, 49,000 in financial and insurance work and 58,000 in professional, scientific and technical activities.