A recent survey found that one in four employers had difficulty finding staff.
A fast-track work permit system to attract immigrants with specialist training to plug gaps in IT and other hi-tech industries has already been announced.
But Ms Roche is expected to hint that reforms should go further in a speech she will give to the Institute of Public Policy Research on Monday.
It could mean the introduction of a US-style green card system that would allow key workers to remain in the UK for the rest of their lives.
A recent survey found that one in four employers had difficulty finding staff.
The information technology sector alone is forecast to need 250,000 people over the next decade.
There are also shortages in areas such as engineering, healthcare, teaching and catering and agriculture.
Earlier this month, the NHS announced it would be drafting in nurses from China in order to meet staff shortfalls.
Immigration 'benefits economy'
Britain faces a demographic time-bomb, with a quarter of the population expected to be over 65-years-old by 2050, Ms Roche is expected to tell the IPPR.
Other countries such as the US, Canada and Australia have used immigration as an economic tool.
Ms Roche is expected to highlight the success such policies have had in America, where officials cite immigration as a key factor underpinning the country's extended economic boom.
And some experts maintain that offering workers the stability of permanent rights to residence rather than short-term work permits is the only way to attract the highly skilled and those prepared to do jobs Britons do not want.
Ms Roche told the BBC's Today programme, "We do live now in a global economy where skilled people are at a premium and it's not always a buyers' market."
'Train Britons' - Tories
But she stressed that no decision has been made on how economic migrants might be admitted, and dismissed reports that up to 100,000 foreign workers a year could be allowed to settle in the UK as "absolute and complete nonsense".
Ms Roche concluded: "This country is a country of migrants and we should celebrate the multi-cultural, multi-racial nature of our society, and the very positive benefits that migration throughout the centuries has brought."
The Conservatives oppose any relaxation of the immigration regulations but say they would look at more flexibility in the work permit system.
They also say the government should focus on properly training the British workforce - something Labour argues is already a priority.