The prime minister will say "progress will not always be smooth" but the UK can "prove the doomsayers wrong".
Following her recent Florence speech in which she gave assurances on payments to the EU and citizens' rights, she will say "the ball is in their court".
Her statement comes as the fifth round of negotiations began in Brussels.
It is the final set of talks before EU leaders meet on 19 October to decide if enough progress has been made to talk about post-Brexit relations with the UK, including trade.
Two White Papers will be published after the PM's statement, covering future trade and customs options.
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In her first address to parliament since last month's speech in Italy, in which she said the UK would honour its financial obligations to the EU budget, Mrs May will describe the government's ambition for a "new, deep and special partnership between a sovereign United Kingdom and a strong and successful European Union".
"And as we look forward to the next stage, the ball is in their court. But I am optimistic we will receive a positive response."
Summit deadline
After a difficult week for the prime minister following her chaotic Tory conference speech and renewed questions about her leadership, the BBC's assistant political editor Norman Smith said she was determined to seize the initiative and adopt a more assertive, bullish tone about Brexit.
The talks between UK negotiators and Brussels officials will be lower profile this week, with neither David Davis or his EU counterpart Michel Barnier attending the start.
European Commission president Jean-Claude Juncker has said it will take miracles for the necessary progress to have been met before the summit, whilst the European Parliament made its voice heard with a non-binding motion saying that more needed to be done.
Around Brussels there is cautious optimism that agreement can be reached on how British judges might interact with the European Court of Justice and how the deal will be implemented.
Chatter concerns whether the final arrangement on citizens' rights can be accorded a status in the UK similar to the European Communities Act, which gave EU rules supremacy over British law - a legal concept called "direct effect."
However, progress on a means of calculating the UK's financial obligations - the "Brexit Bill" - seems much less likely.
The UK will continue to challenge the demands made by EU chief negotiator Michel Barnier.
But the EU side is disappointed that specific British negotiating positions have not emerged after Theresa May's warm words in Florence a fortnight ago.
A European Commission spokesman said there was a "clear sequencing" to how talks would unfold.
"This is not exactly a ball game," Margaritis Schinas said. "There has been so far no solution found on step one, which is the divorce proceedings, so the ball is entirely in the UK court for the rest to happen."
After her speech in the House of Commons, Mrs May will meet with leading industry figures to try and reassure them about the Brexit process.
Companies including Aston Martin, HSBC, Morgan Stanley and Vodafone will attend the meeting of the Business Advisory Council in Downing Street, alongside Chancellor Philip Hammond and Mr Davis.
Mr Hammond has come under fire from some Conservative MPs amid claims the Treasury is talking down the UK's prospects outside the EU.
Bernard Jenkin said the Treasury seemed intent of preserving access to EU markets "at any cost" and the prime minister needed to make clear the current pace of talks was unacceptable.
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