Luxembourg is one of them.
On a visit to Singapore, Luxembourg's finance minister Pierre Gramegna said the country is already a gateway into Europe and poised for a bigger role.
"We have triple-A ratings from all rating agencies. (There is) a lot of predictability and stability politically, economically and financially," he told CNBC's "Squawk Box".
Gramegna has already seen some success.
Insurance giant AIG on Wednesday said it will open a subsidiary in Luxembourg while keeping its main European headquarters in London. But he said that ties with the City of London are still essential.
"Business always finds ways to expand and we want to be natural partners with the U.K. in this new venture," he added.
Luxembourg is also on the Lloyd's of London's shortlist for its EU subsidiary, Reuters reported.
The plans come amid uncertainty about London as the region's financial center as passporting rights and entry to the single market will not be guaranteed after the U.K. leaves the EU.
U.K. Prime Minister Theresa May is expected to trigger Article 50 of the Lisbon Treaty by the end of March to kick off a formal exit. Unraveling Britain's ties with the trade bloc is then expected to take about two years.
The divorce can get messy if the U.K. refuses to pay the exit bill, which will be the first issue to be negotiated, said Jacob Kirkegaard, research fellow at the Peterson Institute for International Economics.
"If the U.K. refuses that, then the EU is going to say in return 'we are not going to be negotiating any future trade relations with the U.K.', at which point there is a real risk these negotiations break down and you may have early elections called in the U.K.," Kirkegaard told CNBC's "The Rundown".
"(This) will create a lot of additional uncertainty and some volatility in the financial markets," he added.