White papers are policy documents produced by the government that set out proposals for future legislation.
May has divided most of her cabinet into two groups to try to improve the two proposals and come to a conclusion over which is best placed to prevent a return to a hard border with European Union member Ireland and ensure trade moves as freely as possible.
Conservative MPs were invited into Downing Street on Monday for a briefing from the PM and chief of staff Gavin Barwell on the "customs partnership", believed to be Mrs May's preferred option, under which the United Kingdom would collect tariffs on the EU's behalf.
Brexit minister David Davis told his cabinet colleagues on Tuesday that the document will be the most significant publication on relations with the European Union since the 2016 referendum.
Asked for the PM's response to Sir Mick's complaint, Mrs May's official spokesman said he would point the veteran rocker to an article in the Sunday Times in which she set out her plans for Brexit.
However, ministers did agree that big decisions had to be taken soon, one official said.
A second option, "maximum facilitation", would involve using technology to minimize customs checks.
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At the same time, Mr Davis has reportedly told the PM that the customs partnership model she favours would be illegal under global law.
The UK attorney general's office is now said to be looking into the legality of both proposals ahead of a final decision by the Cabinet.
Blomfield repeatedly sidestepped questions over whether Labour would back the move when it goes before MPs in the Commons, though sources close to the Labour leader, Jeremy Corbyn, appeared to rule out that possibility on Monday night after a private meeting of Labour MPs.
Britain's opposition Labour Party will try to force Prime Minister Theresa May's government on Wednesday to reveal details of its two customs proposals in Brexit talks, capitalising on a row that is dividing her ministers.
Shadow Brexit secretary Sir Keir Starmer said: "The government's Brexit strategy is in complete and utter deadlock".
A so-called White Paper is likely to outline proposals for future arrangement and outline proposals for specific sectors including financial services, agriculture and cars, according to two government officials.
'However, ministers have wasted months arguing amongst themselves rather than negotiating in the national interest.