Downing Street sources told The Telegraph that Mrs May could ask senior Labour MPs including Hilary Benn and Yvette Cooper to sit on the commission, which would "shadow the work of the Brexit department”.
The news comes after Mrs May asked Labour leader Jeremy Corbyn for his support in securing the legislation needed for Brexit. On Tuesday, she said opposition parties should "contribute, not just criticise” and help "clarify and improve” the Government’s Brexit policies.
Friends of Mrs May said the commission would allow ministers and official to win cross-party backing for a negotiation strategy with Brussels.
Mr Benn and Ms Cooper are both members of the Privy Council, which gives them access to briefings on government work. Neither voted for an amendment backed by Chuka Umunna earlier this month to keep Britain in the single market after Brexit.
Shadow Brexit Secretary Keir Starmer could also be considered for the commission, and the paper reports that David Davis personally pushed for him to becoming a member of the Privy Council, to which he was sworn in last month.
