Speaking at the World Economic Forum in Davos, Khan will say getting a good deal on trading into the Single Market should be May's top priority in her negotiations with the EU.
"It’s critical for London. Nothing else will do. It can’t be brushed aside – as it was yesterday," he will say.
Khan will also warn of the dangers of a "hard Brexit", under which the UK would move to World Trade Organisation defaults on tariffs.
While May has stressed a desire to secure tariff-free trade with Europe, she has also added the UK could walk away from talks if she is frustrated by the EU's negotiators.
“If we continue on this path - towards a ‘Hard Brexit’ – we risk having to explain to future generations why we knowingly put their economy, their prosperity and their place on the world stage in such peril," he will say.
But Khan is also expected to join echo May's warning of Europe being cut off from the financial expertise of the City.
“A ‘Hard Brexit’ would cut Europe off from its only truly global financial centre. This would be bad news for Europe as well as Britain. So a Hard Brexit really would be a lose-lose situation," he will say.
“Tell your political leaders that a ‘Hard Brexit’ deal is not in the best interests of your company. This won’t be easy. But I’m confident that despite the Prime Minister’s rhetoric, there is still a sensible deal to be done.”
The mayor will meet with the Prime Ministers of Sweden and Norway while at Davos, as well as King Phillipe of Belgium and chief executives from Samsung, Hitachi and Mastercard to discuss the capital's position after Brexit.