Sky News understands Environment Secretary Michael Gove has asked the Department for International Development (DfID) to consider increasing the proportion of the £13bn annual overseas aid budget that is spent combating the problem.
:: Fishing for plastic to build litter-picking boats
Speaking in Paris after attending a major climate change summit of world leaders, Theresa May acknowledged greater amounts of overseas aid money could be used to save marine life.
"We've all been very concerned by the pictures we've seen in recent months of the impact of pollution on marine life, the impact of plastic pollution," she said.
"Of course the UK Government has already taken steps in relation to plastic - a charge on carrier bags, a ban on microbeads.
"But we are looking at what more we can do.
"That's not just the Environment Secretary but the International Development Secretary.
"To see how we can use overseas aid money to ensure we're doing what I think everybody wants, which is reducing this terrible pollution that is taking place and affecting marine life so devastatingly."
:: Plastic in sea could be worse than first feared
Meanwhile, a study by the Helmholtz Centre for Environmental Research (UFZ) in Leipzig, Germany, has found 90% of plastic waste entering the oceans comes from just 10 rivers.
Two of them, the Nile and the Niger, are in Africa, while the other eight are in Asia: the Indus, Ganges, Amur, Mekong, Pearl, Haihe, Yellow and Yangtze.
:: Sky has been running a campaign to make people more aware of the effect plastic has on the world's oceans and to share ways of tackling the problem. To get involved in Sky Ocean Rescue, visit the campaign website here. You can also watch our documentary, A Plastic Voyage.