Khan told Sky News the government should wait until after French and German elections next year.
France will chose its next president in May, while Germany is not expected to vote until at least August 2017.
"I lost the argument and now it's for them to persuade the EU how we can get the best of both worlds, how it's possible to have access to the single market and not have free movement of labour,” Khan said.
"Maybe waiting for French and German elections to be out of the way gives the new French president or German chancellor more of a chance for latitude for some of the things that the British public say we need."
Khan added that business leaders from Milan, Paris, Berlin and Dublin are courting business leaders at present.
"At the moment, businesses aren't leaving. At the moment they have hope - they are being reassured by myself and others that we have a plan in relation to getting the best deal possible.
"Once we serve notice then the stopwatch starts, the countdown begins and it becomes more difficult rather than easier,” he said.