PM Cameron makes reform case in Iceland
Iceland and Norway are outside the European Union but are part of the European Economic Area, which allows them to trade in the single market.
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But Mr Cameron is expected to say that arrangement will not work for the UK.
A Number 10 source said Norway accepts some EU rules with little say in the decisions made in Brussels.
Oslo also pays about 600m euros (£432m) a year to the EU.
"Unlike the UK, Norway has no veto in the European Council, no votes in the EU's council of ministers, no MEPs or votes in the European Parliament, and no European commissioner to help," the source said.
Norway is also signed up to Europe's free movement rules, the source said, so a similar arrangement for the UK would do little to reduce the number of EU migrants heading to Britain.
Some British Eurosceptics look to Norway's position as a model for the UK if it were to leave the EU.
BBC political editor Laura Kuenssberg said: "This summit in Iceland will mark a change in David Cameron's tone and pace.
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"Until now he has avoided saying too much about the campaigns to stay and leave - as he tries to get a better deal for the UK inside the EU, and retain the option of leaving if he can't."
'End EU supremacy'
The UK will hold an in/out referendum on EU membership by the end of 2017.
Dominic Cummings, director of the Vote Leave campaign, said his group did not support the "Norway option" for the UK if the public backed severing ties with Brussels in the in/out referendum promised by Mr Cameron.
"After we vote leave, we will negotiate a new UK-EU deal based on free trade and friendly co-operation," Mr Cummings said.
"We will end the supremacy of EU law.
"We will bring back control including over trade deals and migration.
"This is safer than voting to remain which means giving more power and money to Brussels every year."
Mr Cameron is expected to have talks with the leaders of both Iceland and Norway at the Northern Future Forum, a grouping which also includes EU members Denmark, Estonia, Finland, Latvia, Lithuania and Sweden.
The prime minister's official spokeswoman said the meeting in Iceland was an opportunity for Mr Cameron to have discussions with EU leaders about the UK re-negotiation.
"That is what the PM is focused on," she said.
"He has been clear that he thinks there are reforms we can secure to address the concerns of the British people and that it is the UK's interest to be in a reformed EU."