The Prime Minister will tell MPs that the "ball is in the EU's court" when she updates them on the progress of Brexit negotiations.
And as she aims to move on from her disastrous conference speech, she will declare the United Kingdom can get a deal to prove the anti-Brexit "doomsayers" wrong.
The embattled May is set to tell parliament on Monday that she expects "leadership and flexibility" from the other 27 European Union countries in the negotiations.
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Jean-Claude Juncker, the European Commission president, said last month that it would take a "miracle" if talks are to progress to trade, while the European Parliament passed a non-binding motion declaring that more needs to be done.
Mr Davis' no-show comes just hours after Theresa May's team briefed journalists that her Florence speech contained all the compromises she is willing to make, adding that the "ball is now in the EU's court". According to her, they are working hard to attain the status of the free-trading nation and she is very much optimistic about it. "I believe we can prove the doomsayers wrong".
"Because what we are seeking is not just the best possible deal for us - but also the best possible deal for our European friends too".
"The Business Advisory Council is an important part of our preparations for leaving the European Union - allowing us to seek the views of experienced business leaders and to share with them the government's vision for a successful Brexit".
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Representatives from firms including Aston Martin, HSBC, Morgan Stanley and Vodafone will be among those attending.
The meeting follows warnings from RBS chairman Sir Howard Davies that the damage to the City from Brexit is "going to be quite considerable over time".
If they don't agree then they wouldn't get another chance until a summit in December before leaving the bloc formally on March 29, 2019.
The leading Leave supporter said the Treasury had an "institutional mindset" when it came to Brexit, but insisted he was not making a personal attack on the Chancellor.
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Senior ministers - including Johnson - rallied around over the weekend and rumours swirled of a forthcoming cabinet reshuffle in which May could assert her authority.