The development comes after EU leaders last week signed off on the first stage of Brexit negotiations ending more than a year of stalemate over Britain's bill for leaving the bloc, as well the fate of the Irish border and EU migrants.
Barnier will table his proposals to the college of commissioners, which unites representatives from the 28 member states and the European Commission, the EU's executive arm.
Once agreed, negotiations can then move on to future relations for the longer term, with Britain hoping to complete a trade deal as early as possible.
Barnier is widely expected to demand a transition that obliges Britain to adhere to all EU rules, but without a say, during a period of around two years.
"Commission negotiators will argue that the UK will have to replicate EU membership in all its facets," said Mujtaba Rahman of Eurasia Group, a risk consultancy.
May has already accepted in theory the continued jurisdiction of the European Court of Justice in the transition and that London will have no legal basis to conclude its own trade deals during the period.
Leading conservative lawmaker Jacob Rees-Mogg slammed this demand as "rather hostile", leaving the UK "no more than a vassal state, a colony, a serf of the European Union".
May insisted to British lawmakers on Monday that the transition is necessary as it would provide continuity for businesses and individuals until the future relationship could be resolved.
Given the potential pitfalls, "although May will be reluctant to extend Article 50 negotiations or the length of the transition ... there is a significant probability she will have to," said analyst Rahman.
The next phase comes as Barnier ruffled feathers in London yesterday with a warning that any ties after Brexit would inevitably result in Britain's financial companies losing full rights to trade across the bloc.
This was a consequence of "the red lines that the British have chosen themselves. In leaving the single market, they lose the financial services passport," Barnier told a group of European newspapers.
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