A director at an asset management firm owned by one of France’s big banks, she asked to stay anonymous, but told CNBC that even her husband, a portfolio manager, was on the lookout for work in Singapore.

She added that they would move to the city-state with their two children as soon as one of them lands a job.

“Singapore seems like a very green field compared to Paris,” she said. “It looks like what Europe was 20 years ago, in the sense it’s got a lot of opportunities in terms of new prospects for the markets.”

The French investment banker is one among a growing number of bankers looking to leave Europe as deteriorating economic conditions together with tougher regulations have slowed business and led to job cuts.

“It’s very, very slow here [in Europe]. On top of that, there are a lot of regulations adding up on each other, so it makes things a bit difficult,” she said.

Several global recruitment firms have told CNBC they’ve seen a significant increase recently in the number of European bankers wanting to relocate to the Southeast Asian city-state.

According to Stella Tang, Director at recruitment agency Robert Half, there has been a 20 percent increase in investment banking applicants from Europe since 2009, with Europeans now overtaking the Americans.

At recruitment firm Hudson, more than 50 percent of inquiries for Singapore-based finance jobs have been coming from Europe since September last year, with the majority of applicants looking for investment banking roles.

“The market conditions in places like Europe and the U.K. continue to deteriorate and there is a perception out there that market conditions are significantly better in Singapore,” Craig Brewer, Director of Banking, Financial Services & Legal at Hudson said.

Though Singapore has very close trade and financial links with Europe and there are worries that a further escalation in the euro zone debt crisis could push its economy into turmoil, firms in the city are still hiring.

“The drive to hire is strong among the largest ones [companies], where 45 percent of them said [in a survey] they are increasing their head count this year,” Tang said.

But despite the bullishness over Singapore’s job market, Tang adds that the financial center has not added a huge number of investment banking jobs over the past year, and Europeans coming here have had to take a salary cut.

“When U.S. or U.K. investment bankers come to Singapore or Hong Kong, they will have to take a pay cut. The pay cut could be anything between 10 to 30 percent,” she said.

Andrew Norton, Regional Managing Director South East Asia, at Michael Page International backs that trend saying he’s seen bankers from Europe willing to relocate without expatriate packages that include housing and school allowances.

He adds that what they lose out in terms of perks gets compensated by the low tax rate in Singapore. “In fact, some of these candidates find themselves in a better-off position compared to when they were in the U.S. and Europe,” he said.

Asian Bankers Returning Home

The slowness in European and U.S. markets is also leading to more Asian-born bankers returning home to work, according to Norton.

“They [Asian-born bankers] feel the risk-reward trade-off is better and that they can add more value through local expertise and language skills,” Norton said.

Malaysian-born Wai Keng Kwok, 33, is one Asian-born banker looking to make a fresh start in Singapore. Kwok moved to the island-nation in February, after working for Morgan Stanley in New York for five years, to take up the role of chief operating officer at a local hedge fund started by a friend.

Kwok says she decided to move to Singapore to be closer to her parents living in neighboring Malaysia and because she didn’t think she would be able to get the same level of entrepreneurial opportunity elsewhere, particularly in Europe.

“Out of Southeast Asia, I believe Singapore is the only place that’s really going to offer the same level of finance jobs that I would have gotten say in New York or London,” Kwok, a Yale and INSEAD graduate, said.

With the recent cutbacks by U.S. and European banks, Kwok says it’s nice not to have to constantly worry about losing your job.

“You don’t have to contend with the doom and gloom I suppose that people in New York and Europe face, because I don’t think there’s the same amount of pessimism here,” Kwok said.

The French investment banker looking for a job in Singapore adds that she is not going to go anywhere else.

“Singapore overall is a very friendly Asian place compared to all the other ones. It’s not only number one, there’s no number two,” she said.

- By CNBC's Rajeshni Naidu-Ghelani