Theresa May is to tell the two men vying to replace her as prime minister that they must make strengthening the union one of their top priorities.
In a speech in Scotland on Thursday, Mrs May will urge her successor to “think creatively” about how to ensure the UK stays together.
She will also give further details of a review into how devolution is working.
The review is aimed at ensuring UK government departments are working in the best interests of devolution.
The government has stressed it will not include devolved areas that are the responsibility of the Scottish government.
Scotland’s first minister, Nicola Sturgeon, predicted ahead of the prime minister’s speech that the review was “too little, too late” and would do nothing to prevent Scottish independence.