Some parts of rural Britain have just one or two of the main mobile phone networks available, or none at all, leaving some people without any signal.
It is hoped so-called national roaming could be used to plug blackspots.
However, mobile phone companies say this would remove their incentive to build more masts to improve coverage.Existing legislation
National roaming would allow phone users to switch to an alternative network if their own was not available, as happens when they are abroad.
A spokesman for the Department for Culture, Media and Sport, which oversees telecommunications, said the government was already spending £150m in areas with no coverage and was looking at doing more.
A mobile phone industry source told the BBC the government might be able to force the big operators to share their networks using existing legislation.
But the companies are likely to argue that national roaming will be a brake on their investment because there will not be an incentive to build new phone masts in remote areas if the service has to be shared.