The new force would merge existing bodies including the British Transport Police, Civil Nuclear Constabulary and Ministry of Defence Police, The Times quoted senior government sources as saying.
"It is not always clear who should deal with a suspect package in a station for instance. The need for a clear line of command has been obvious for many years but is more pressing, given the threats we are seeing now," one source told the newspaper.
In one model under consideration, the new force would be split between an unarmed and an armed unit, with about 6,000 in the former and 4,000 guarding the most sensitive sites and providing a rapid response unit.
Under that model, the armed officers would include the British Transport Police but not, as originally intended, Highways England's enforcement arm.
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As well as airports and key sea ports the new force would oversee the rail network and some roads.
An alternative model would create two separate forces, one dealing with nuclear and military assets and the other focused on transport hubs.
British Prime Minster Theresa May is expected to take a final decision on the new force by early next year.