The idea, long advocated by some senior figures in Brussels, would help people left “heartbroken” by departure from the European Union, the mayor of London said.
It would allow British citizens to retain the right to free movement between EU member states after the end of the transition period, in December, as well as voting rights for the European parliament.
Mr Khan put the plan forward as he prepared to meet Michel Barnier, the EU’s Brexit negotiator, and after the two sides stepped up their war of words before trade talks begin.
“I am heartbroken that we are no longer a member of the European Union, but that doesn’t mean our country’s future can’t be closely linked with the rest of Europe,” he said.
“The prime minister says his job is to bring the country together and move us forward and I cannot think of a better way of reconciling the differences between British voters who wanted to leave, and the millions of Londoners and British nationals who still feel and want to be European.
“There would be support from millions of Londoners and British nationals who are devastated they are losing their rights as EU citizens.
“As the UK and EU start their next phase of negotiations, I want this issue of associate citizenship to be at the heart of talks about our future relationship.”
Guy Verhofstadt, the European parliament’s Brexit coordinator before the UK’s departure, has long campaigned for “associate citizenship” for people angry at losing EU privileges.
Mr Verhofstadt said: “The Maastricht Treaty created the concept of ‘European citizenship’ and I am in favour of using this now as a basis for people who want to keep their link with Europe.
“It is the first time in the history of our union that a member state leaves, but it is not because the UK government wanted exit that individual citizens have to lose their connection with the continent.”
But Rory Stewart, the former Conservative candidate running as an independent in May’s mayoral election, attacked the policy as “only a sound bite”.
“The policy cannot work. The mayor has a responsibility to produce a much more detailed position on Brexit – that protects London. I have such a plan.”