Ahead of a visit to Brussels on Tuesday, the Mayor of London urged the Government to allow all British nationals to have 'associate citizenship' of the EU.
This would allow British citizens to keep many of the rights they held before Brexit, including the right to move freely between EU member states.
Mr Khan said: "Like so many Londoners, 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.
"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."
Mr Khan will meet the EU's chief Brexit negotiator, Michel Barnier, and the president of the European Parliament, David Sassoli, during Tuesday's visit to the Belgium capital.
The idea of European citizenship has been backed by the former chairman of the European Parliament's Brexit steering group, Guy Verhofstadt.
He 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."
Shaun Bailey, the Tory candidate in the upcoming mayoral election, claimed Mr Khan was focusing on "gimmicks" rather than dealing with crime in London.
Mr Bailey said: "Three more Londoners were stabbed on the weekend and a teenager is fighting for his life as we speak, and where is our mayor?
"In Brussels, announcing a gimmick he has no powers to implement."The mayor has got to focus on his actual responsibilities; he should be in London, urgently speaking with the Met Police, over whom he does have actual powers, about how to stop kids being stabbed to death on our streets."We need a change in leadership, we need a new mayor whose priority is keeping Londoners safe."Rory Stewart, independent candidate for London Mayor, added: "This is only a soundbite - 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. And if I were mayor I would be focused on making detailed arguments about a future immigration system, as well as service agreements, to keep London as close as possible to Europe."I would win these arguments with the Government and with Brussels with evidence, not soundbites. And I would also fix many of the things, including safety, which have gone in the wrong direction over the last four years in London. We need less talk from this mayor and more action".