May has said she wants to invoke Article 50 of the EU's Lisbon Treaty by the end of March 2017, setting in motion two years of formal talks on the UK's departure from the bloc.
In that time, the government will have to draw up new rules for a range of economic activities currently governed by EU regulations as well as strike new trade deals.
If no agreements are reached, trade between the UK and the EU would be governed by World Trade Organization rules.
The CBI conference precedes Chancellor of the Exchequer Philip Hammond's Autumn Statement on the economy Wednesday, when he will outline the government's near-term priorities for tax and spending.
Many business leaders favored staying in the EU. Since the June 23 vote went the other way, the CBI has led calls for the UK to maintain tariff-free ties to the bloc, while ensuring that British companies can continue to tap workers from the EU.
We want to get the arrangement that is going to work best for the UK and that will work best for business in the UK.
May has pledged to curb immigration, a principal demand of the "Leave" campaign -- but one that EU leaders have said is incompatible with continued single-market access.
So far May has yet to provide a detailed roadmap of the government's Brexit plans. Executives at companies ranging from UK advertising giant WPP Plc to US bank JPMorgan Chase & Co. have warned that uncertainty has hamstrung business.
May told the CBI on Monday that she would not provide a "running commentary" on the Brexit negotiations.
Drechsler said business leaders understand the need for discretion but just want more clues as to May's intentions.
"We're not asking for a running commentary, but we are looking for clarity and, above all, a plan," he said.