Chancellor George Osborne will unveil the plan when he sets out measures intended to make Britain the "global centre of financial innovation".
Bitcoin is not controlled by a central bank but is growing in popularity.
Other measures will include plans to make it easier for businesses to get loans from sources other than banks.
The measures will help firms to "grow and succeed", Mr Osborne will say in a speech.
How Bitcoins work
Bitcoin is often referred to as a new kind of currency.
But it may be better to think of its units as being virtual tokens that have value because enough people believe they do and there is a finite number of them.
Each bitcoin is represented by a unique online registration number.
These numbers are created through a process called "mining", which involves a computer solving a difficult mathematical problem with a 64-digit solution.
Each time a problem is solved the computer's owner is rewarded with bitcoins.
To receive a bitcoin, a user must also have a Bitcoin address - a randomly generated string of 27 to 34 letters and numbers - which acts as a kind of virtual postbox to and from which the bitcoins are sent.
Since there is no registry of these addresses, people can use them to protect their anonymity when making a transaction.
These addresses are in turn stored in Bitcoin wallets, which are used to manage savings. They operate like privately run bank accounts - with the proviso that if the data is lost, so are the bitcoins contained.
Speaking at London's Canary Wharf later, the chancellor will say that it is "only by harnessing innovations in finance, alongside our existing world class knowledge and skills in financial services, that we'll ensure Britain's financial sector continues to meet the diverse needs of businesses and consumers here and around the globe".
As part of the drive, he will announce the government is to investigate the potential for virtual and digital currencies such as Bitcoin to encourage innovation in the UK's financial sector, while also examining their potential risks.
More than 60,000 online retailers now accept virtual currencies worldwide and the growing popularity has seen backers of the currencies push for greater mainstream adoption. However, their use has also been linked to illegal activity online.
BBC technology correspondent Rory Cellan-Jones said: "Enthusiasts say it is the future of money, detractors claim that it is extremely volatile and is used mainly by drug dealers and money launderers.
"Now the government says it will examine whether this and other virtual currencies should be regulated, how they could help stimulate innovation - and their potential risks."
Mr Osborne will also outline plans to introduce legislation to help small and medium-sized businesses access alternative sources of finance if they have been turned down for finance by their bank.
He will say the government will encourage the growth of "alternative finance providers" - a major part of the financial and technology, or FinTech sector.
Business Secretary, Vince Cable said small businesses often "give up" applying for finance if they have been turned down by a bank.
He said money was "already reaching small businesses", but said the UK needed a "diverse and competitive business finance market like Germany and the US".
The government will publish a strategy document later this year setting out how it intends to make the UK the global centre of financial innovation