Under the plan, detailed in The Sunday Times, Mr Johnson will try to agree a new deal with Brussels at a summit on October 17.
But should he fail he will then reportedly refuse to comply with the anti-No Deal legislation passed by MPs and ignore the requirement to ask for an extension.
Downing Street believes such a course of action will guarantee an immediate judicial review in the Supreme Court with the fate of Brexit placed in the hands of judges, just days before the October 31 deadline.