"It looks like the cake philosophy is still alive", Tusk said, referring to earlier comments by British officials that they wanted to "have their cake and eat it" when it came to leaving the EU's single market and enjoying its benefits.
Confirmation of the much-anticipated speech comes after May gathered around a dozen of her senior ministers for an "away day" at her country retreat in Chequers yesterday.
The UK has agreed its negotiating position for Brexit after an eight-hour meeting between the senior political leaders to thrash out their differences, ministers said.
He dismissed the flagship idea of "managed divergence" from European Union law after Brexit, which is also known as the "three baskets" plan as proof that the British still wanted, as Boris Johnson once said, to have their cake and eat it too. From the very start it has been a key principle of the European Union 27 that there can be no cherry-picking and no single market a la carte.
Many businesses and investors complain that they still lack details on how trade will flow between the world's biggest trading bloc and its sixth largest economy after Brexit.
The single market guarantees free movement of goods, capital, services and people - the "four freedoms" of the EU - while the customs union provides for tariff-free trade among the 28 member states but requires that the bloc of 500 million consumers negotiates trade agreements overseas as one, rather than as individual European states doing bilateral deals.
Polish Prime Minister Mateusz Morawiecki, whose country is the biggest beneficiary of European Union funds, said: "We want (policies) that have so far worked well for Poland... to be continued".
But one source close to the meeting at Chequers said May had accepted the argument of those ministers who wanted to move away from European Union rules and regulations more quickly than others.
In those circumstances, Mr Blair said, "the case is ever more stronger for this going back to people to allow them a final say in the deal that is actually agreed by the Government".
These "red lines", however, appear to be irreconcilable with Britain's pledge not to re-introduce a physical border between Northern Ireland and Ireland or to give its companies, including banks, as full access as possible to the EU's market.
The rifts are mirrored across Britain where the debate over plans to leave the European Union after the June 23, 2016, vote has become increasingly angry and divisive.
The government said the report was at a "preliminary" stage when it was leaked in January and refused to publish its analysis in full, but Brexit critics argue that a departure from the single market will inevitably cost the United Kingdom large sums of money.
And the opposition Labour Party is widely expected to throw its weight behind a close customs union deal when its leader Jeremy Corbyn outlines his priorities in a speech on Monday.