The BBC wants to increase the licence fee by 2.3% above inflation to boost its programmes and digital services.
The BBC's bosses have made a series of shake-ups to cut costs
The corporation is to present its bid for the next licence fee settlement to a House of Commons select committee.
If the government accepts the BBC's proposal, the fee would rise by £3.14 per year until 2013, not including inflation. The current fee is £126.50.
BBC director general Mark Thompson said the rise would fund the switch-over to digital TV and BBC on-demand services.
The BBC says it needs an extra £5.5bn over the next seven years to pay for more original programmes, new digital and local services and increased costs.
COST OF BBC PLANS
Content quality £1.6bn
Eg - cutting repeats
Digital services £1.2bn
Eg - TV and radio on internet (above)
Digital infrastructure £0.7bn
Eg - high definition TV
Local relevance £0.6bn
Eg - regional TV and radio
Base costs £1.4bn
Eg - sports rights
The corporation says it can fund £3.9bn of that through cost-cutting measures and commercial profits. But the proposed licence fee increase would fund the remaining £1.6bn.
"We know that licence fee payers find the licence fee a burden in their household costs," Mr Thompson said.
"But on the other hand, we also know that they are overwhelmingly in favour of the BBC spearheading these new digital services.
"It is a bigger licence fee, but the BBC gives out of it bigger digital TV and digital radio services. It is a big step towards digital Britain."
The corporation's valuation kicks off negotiations that will eventually see the government set the new annual fee.
The current deal ends in April 2007 and the next will last for seven years. The licence fee currently generates £2.94bn a year for the corporation.
Under the current deal, set in 2000, the licence fee goes up by 1.5% above inflation per year. It will increase to £128.50 next year, not allowing for inflation.
Culture Secretary Tessa Jowell has said the corporation will get some extra money to spearhead the UK's switch to digital TV by 2012.
The corporation aims to make its TV programmes available on the internet, to make its archive more accessible and invest more in local TV and radio services.
The BBC has also pledged to show fewer repeats and move some of its operations out of London - although a planned move for some of its departments, including sport, children's productions and Radio Five Live, to Manchester may depend on the licence fee settlement.
Mr Thompson and BBC chairman Michael Grade have already made a series of shake-ups, including almost 3,800 job cuts and internal value-for-money drives.
But culture select committee member Nigel Evans MP said: "There are millions of people out there who don't get inflation-busting increases whatsoever."
"How have you got the nerve to come here and say you want to push up the licence fee to near £180 and expect those people to stump up the cash?
"There is a poll tax on their TVs and they have got to pay it."
The BBC said research found 81% of the BBC audience believed the licence fee was good value for money and more than 40% would be prepared to pay twice the current licence fee or more.
The negotiations come as the government prepares to set out the corporation's role, function and structure in its next 10-year royal charter, which will also come into force in 2007.