British employers have started to push harder for a Brexit deal that causes as little disruption as possible after voters failed to back Prime Minister Theresa May's tough approach to divorce negotiations with the EU in an election last month.
The result, which cost May her majority in parliament, has reopened the debate about how Britain should leave the EU.
"Instead of a cliff edge, the UK needs a bridge to the new EU deal," Carolyn Fairbairn, the CBI's director-general, was due to say in a lecture at the London School of Economics.
"Even with the greatest possible goodwill on both sides, it's impossible to imagine the detail will be clear by the end of March 2019," she said.
Many firms are worried about losing some of their access to markets in the EU and facing barriers to hiring workers once Britain leaves the bloc in less than two years' time.
"This is a time to be realistic," Fairbairn said. "Our proposal is for the UK to seek to stay in the single market and a customs union until a final deal is in force."
Fairbairn said the CBI's proposal would mean that firms would only need to cope with one transition, not two, which should be "limited" in duration.
The possibility of disruption had already caused a major European engineering and electronics firm to shelve its plans to build an innovation center in Britain, she said.
Fairbairn did not discuss what Britain would need to do in order to remain temporarily in the single market, but it would probably mean continuing to allow free entry to EU migrant workers and observing rulings of the European Court of Justice.
Brexit supporters focused on the need for immigration controls and to break free of the ECJ ahead of last year's referendum, and one pro-Leave campaigner said the CBI proposal threatened to override the decision of voters.