The multi-billion pound "interconnector" could allow geothermal energy from Iceland to be pumped directly to Britain.
On a visit to Iceland, David Cameron, who is the first British Prime Minister to visit Reykjavik since Winston Churchill in 1941, will announce a task-force has been established to examine the feasibility of the project.
If there is a successful outcome then the giant hydro-electricity cable between the two countries could be built within a decade.
Iceland gets around 95% of its power from hydro and geothermal energy. Officials said that establishing a long-term source of renewable energy for Britain would provide greater security.
There are continuing threats of power blackouts because of the lack of energy capacity.
Homeowners were warned earlier this year they could face higher energy bills again this year because of the closure of some power stations.
Mr Cameron has been holding talks about establishing closer energy ties with his Icelandic counterpart Sigmundur Davio Gunnlaugsson ahead of the Northern Future Forum which joins the UK with leaders from Scandinavia and the Baltic states.
Ministers have been in talks with Iceland over the possibility of harnessing the country's geothermal power since 2012.