Downing Street said a Cabinet sub-committee is considering a range of options to limit access to benefits, health care and housing. It indicated one of these was linking a person's entitlement to benefit to their connection to an area through, for example, birth or education.
Foreign Secretary William Hague has made clear the Government is keen to do what it can to tackle the issue, saying: "It is important there aren't artificial, perverse incentives for people to come to the UK."
However, a spokesman for the Scottish Government told The Herald: "Immigration policy is currently reserved to the UK Government. As proven already in recent years, Scotland's public services are well-equipped to deal with migration."
The move to tighten the rules has come about due to fears of an influx of migrants from Bulgaria and Romania as at the end of the year work restrictions on them will be lifted.
Eric Pickles, the Communities Secretary, said: "We've been urging local authorities to give priority to people coming out of the Armed Forces. It does seem to me to be immensely sensible to ensure that if you work in an area or you've got a big connection – you might have been educated there or your family might be nearby – to receive some kind of priority in social housing."