European Union chief negotiator Michel Barnier, however, plans to reject the UK's ideas, saying they would rob Brussels of autonomous decision-making ability.
In an uncompromising statement, Barnier "major issues" are yet to be resolved with regards to Britain's future relationship with European Union following talks with Raab in Brussels.
Mrs May hopes free trade in goods can go on and, if Brussels says no, tariffs could be imposed under World Trade Organization rules.
Britain is attempting to inject new impetus into the talks process after Mrs May's controversial Chequers plan was set out in a White Paper.
In Brussels, officials will discuss the future relationship, the Ireland-Northern Ireland situation and the remaining issues in the withdrawal agreement.
Negotiators are meeting in Brussels this week to address the question of the Irish border. Indivisibility of the four freedoms, the integrity of the single market, these are key points.
Theresa May said the British public should take "reassurance and comfort" from Government preparations for a no-deal Brexit after it emerged plans were being developed to stockpile food and medicines. "Everybody can see that this debate is not yet over".
According to Guardian, the visit scheduled for Monday, July 23, was to show the United Kingdom government's support for the "northern powerhouse" concept and May was set to confirm that funds worth £780 million were being kept aside for a planned east coast mainline upgrade and that the "North of Tyne" deal was to proceed.
Asked if this meant British politicians could still decide to keep the country in the European Union on its current terms, she replied: "Sure, of course".
The Bill also includes provisions for the UK's accession to the plurilateral WTO Government Procurement Agreement (GPA) in order to secure continued liberalised access to foreign government contracts. Under current rules the European Union has sole authority to cut access off at 30 days' notice - a setup banks say is unwieldy, not good for financial stability, and can be open to political meddling. The legislation is being processed in the House of Lords and will undergo a second reading in September. The UK has also formally requested to join the GPA post-Brexit and recently submitted a market access offer on the same terms as those enjoyed by the European Union, which GPA parties are now considering.
The Pound-to-Euro exchange rate is meanwhile widely expected to break below the 1.10 level on a no-deal Brexit, abandoning a long-held sideways range that has seen it trade between 1.11 and 1.16 over the past 11 months.
Both men confirmed they are still aiming for a deal to be signed by October, despite "obstacles" remaining. Without that in place, negotiators can't move on to talks on the future trade terms.
Raab said he believed a so-called "backstop" clause in the treaty on Ireland could be agreed, though he said Britain would insist it was not valid forever - something Barnier says it must be in case Britain's promised better proposals do not work. "What we will make sure, and the idea that we only get food imports from one continent is not appropriate, but we will look at this issue in the round and make sure there is adequate food supply".