Experts from groups including the CBI and BusinessEurope will stress the need for a transitional deal that preserves the status quo after Brexit.
They will urge the government to clarify the future relationship between the UK and the rest of the EU.
The next round of Brexit talks is due to start in mid-December.
They will meet Mrs May at No 10, as well as Business Secretary Greg Clark, Brexit Secretary David Davis and Economic Secretary to the Treasury Stephen Barclay.
The CBI and the Institute of Directors will be represented, as will business organisations from France, Germany, Spain, Italy, the Netherlands, Ireland, Sweden, Poland, the Czech Republic and Belgium.
CBI director general Carolyn Fairbairn told the BBC that it was an important meeting. "The urgency that's shared by business across Europe is growing by the day."
She said a CBI survey showed that 10% of firms had "already pressed the button on their contingency plans" in the event of a no-deal Brexit.
"A firm I spoke to in Belfast last year, who a manufactures in Belfast, because of tariffs and red tape that would result from a no-deal Brexit, they have pulled together plans for moving to France, so it's that kind of contingency plan that firms are putting together."
And the pace of planning by firms was picking up, she added, with about 60% of firms saying they would have implemented contingency plans by the end of next March.
"Which is why getting to a transition arrangement by the end of the year is such an important priority, not just for UK firms but for firms across the European Union."
But there are concerns that future trade talks could collapse ahead of December's EU summit.
EU chief negotiator, Michel Barnier, has warned that the talks will only go ahead if the UK first clarifies its financial obligations to the EU.
Mr Davis has said the UK was "ready and willing" to engage with Brussels "as often and as quickly as needed".
The business leaders are set to tell the prime minister they want real progress on a future free trade agreement, as well as a transitional arrangement until that can be implemented.
Mrs May is expected to reiterate the UK's commitment to securing an implementation period of about two years once the country leaves the EU in March 2019.
She will also ask the business experts to share their input on how the UK and EU can continue to thrive side by side in industry and economic development.
The BBC's business editor, Simon Jack, says some UK business leaders in favour of Brexit are concerned that a transition period maintaining the current arrangements will delay and frustrate Britain's attempts to strike new independent deals.
Our editor says that while hoping a deal with the EU can be achieved, some are concerned that the lack of progress so far plays into the EU's hands.
They are therefore recommending the government uses its time to prepare for a "no deal" scenario which would see the UK trade with Europe on the same terms - and tariffs - as the rest of the world.
Source: BBC News