Earlier, May's spokesman said she stood by her commitment to resign after she completed "phase one" of the Brexit process, or the divorce deal, before handing over to a new leader to negotiate future trade ties with the bloc.
She is immune from a leadership contest until December after surviving one a year ago. The party, which backs a new referendum that would give voters with the option of remaining in the European Union, saw its vote share soar in local elections last week.
Yesterday she met the chair of the influential 1922 committee of backbench Tory MPs who had been demanding that she name the date of her departure.
The leaflet links to a website that names the MPs who voted against Mrs May's deal, according to The Times, including 34 Tory Brexiteers.
Meet Archie ... royal newborn who won't have a title
The name Archie may be short for Archibald, though there's no official word from Buckingham Palace that this is the case. Asked who the baby takes after, she said: "We're still trying to figure that out".
"This is not an issue about me and it's not an issue about her".
Last week, polls placed the Brexit Party ahead of the Labour Party and Conservative Party with 30 percent of Brits votes for European Parliament voting intentions.
A Labour spokesman said: "After the second day of talks this week, the negotiating teams are working to establish scope for agreement, and will meet again at the beginning of next week".
If their talks fail, May has pledged to allow the parliament to decide on a new strategy in a series of votes.
The UK was due to leave the European Union on March 29, but as no deal was agreed by Parliament, the European Union extended the deadline to October 31.
The UK PM's preferred option is to agree a deal with Labour that can be written into a Withdrawal Agreement Bill - the legislation needed for Britain to leave the EU with a deal - which would then be put to a vote by 22 May, before European elections.