Carolyn Fairbairn, director general of the Confederation of British Industry (CBI), will warn the Government that time is running out to make progress on Brexit and urge the Prime Minister to put replicating the customs union at the top of the trade agenda.
"This is a time — we believe — for revisiting some of the red lines," Fairbairn told Sky News.
"If there is one thing business knows about, it's about negotiations and it's not the opening position that matters, it's the closing position that matters.
"This is a time, particularly as we know how urgent the decisions are, for revisiting.
"(With (Other OTC: WWTH - news) ) the customs union, there have been doors that have been left open along the way.
"Let's take them because the business case, the common sense pragmatic case, for a customs union with the EU — negotiated effectively — is very strong.
"It's about jobs in the Midlands. It's about small manufacturers that need to trade in a friction-less way."
Fairbairn will also tell the Government in the major speech on Monday that business needs a transition deal in place by March, with the outline of a final deal signed with the EU by October.
"We need to end this game of who-blinks-first and instead find a new spurt of urgency," Fairburn will tell her audience at Warwick University.
"The UK team can't agree with itself, let alone with the EU. There's too much ideology, too little urgency."
The UK and EU have agreed to a two-year transition period when Britain leaves the EU in March 2019.
But the two sides have yet to agree the terms of that relationship or even discuss what a post-Brexit trade deal will look like.
May said last year that Britain was leaving the customs union but would seek to either "reach a completely new customs agreement to become an associate member of the customs union in some way, or remain a signatory to some elements of it".
But the issue deeply divides her cabinet.
Many Brexiteers are opposed to remaining in customs arrangements with the EU for fear it would hamper Britain's ability to strike free-trade agreements with other countries.