The move follows a meeting with Peter Hain who left his post as shadow Welsh secretary to back the project.
The barrage from the Vale of Glamorgan to Somerset would provide 5% of the UK’s electricity and create 20,000 construction jobs.
It is understood much of the funding for the scheme would come from Kuwait and Qatar.
Hain told BBC Wales:”We had a very good meeting – the prime minister promised to look into it.
“It was a more productive meeting than might have been expected. It’s encouraging that Number 10 are taking the barrage much more seriously than has been the case over the last few years.
“Government support is an absolute pre-requisite for getting the whole project underway.
“Not a penny of taxpayers’ money would be needed for this £30bn investment, which would be transformative for Wales.
“It would create 20,000 jobs in construction and another 30,000 in activity around the barrage.”