Three judges have ruled that Theresa May cannot invoke Article 50 - to start formal exit negotiations with the EU - without Parliament's support.
But sources told the BBC that Mrs May will tell Jean-Claude Juncker she still intends to start the process by March.
The Supreme Court is expected to hear the government's appeal next month.
The BBC's political correspondent Iain Watson says Mrs May is due to outline her commitment during a telephone call to Mr Juncker later.
