The Government is considering banning gazumping, which could stop 200,000 UK house sales falling through every year.
The Telegraph reports that the Department for Business Innovation and Skills floated the idea in a meeting last week with the National Association of Estate Agents.
BIS said it wanted to bring England in line with Scotland and make house sales legally binding earlier in the process than they are now.
In Scotland, offers are legal when the buyer accepts. In England and Wales, this happens when contracts are exchanged.
The news comes ahead of a call for evidence on improving the homebuying process that BIS will launch in the coming weeks.
The call for evidence was first announced in the Budget earlier this year.