The prime minister is expected to tell her party's spring conference that Britons are "at heart one people" be they Welsh, English, Scottish or from Northern Ireland.
It follows Nicola Sturgeon's demands for a second independence referendum for Scotland.
Mrs May has already rejected the call from Scotland's first minister.
Scotland voted to remain in the UK in 2014 but the SNP administration in Edinburgh wants a fresh vote as the UK plans to leave the European Union.
Scottish voters opted by a majority to remain in the EU, with England and Wales voting to leave.
Mrs May said on Thursday it was "not the right time" for another independence referendum.
In her speech on Friday, she will also say she wants to see a fairer society and a stronger economy across the UK.
Last year's Brexit vote was also a vote for changing the way the country works, she will say.
"It means forging a more united nation, as we put the values of fairness, responsibility and citizenship at the heart of everything we do, and we strengthen the bonds of our precious union too," she will tell the conference.
"It means building a stronger, fairer Britain that our children and grandchildren will be proud to call home."
The union is "more than just a constitutional artefact," she will add. "It is a union between all of our citizens, whoever we are and wherever we're from."
She will also promise to take account of competing demands from Wales, Scotland and Northern Ireland as the negotiations begin on leaving the EU, saying: "We are four nations but at heart we are one people."
Meanwhile, the Conservative's leader in Wales, Andrew RT Davies, has accused Labour and Plaid Cymru of "wallowing in self-pity".
He said the situation had got worse since the referendum vote with First Minister Carwyn Jones and Plaid leader Leanne Wood being in "complete denial" over Brexit.
"They cannot get their head around it because they do not want it to happen," the South Wales Central AM said.
Mr Davies said they acted as if "everyone is picking on Wales" when the nation had a great future in store.
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