"She needs to go with dignity, if she sets a date for her departure she can be remembered as the woman who delivered Brexit", said one.
The EU guidance echoes the briefing provided to MPs at Westminster before Thursday's vote, which said "if the United Kingdom were to seek an extension beyond July 1, and hence remain a member state beyond that point, it would need to participate in the EP elections".
After two-and-a-half years of tortuous divorce negotiations with the European Union, the final outcome is still uncertain with options including a long delay, exiting with May's deal, a disorderly exit without a deal or even another referendum.
Theresa May then narrowly saw off a bid by MPs to seize control of the Brexit process.
Party members met with UK Chancellor Phillip Hammond yesterday, fuelling speculation the DUP will seek more funding for Northern Ireland in order to secure its support.
Mrs May's deal, an attempt to keep close relations with the European Union while leaving the bloc's formal structures, was defeated by 230 votes in parliament on Jan 15 and by 149 votes on March 12.
May's spokesman said the government was still making preparations for a no-deal exit.
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Downing Street said this was a "natural consequence" of Mrs May's decision to offer a free vote on an issue where there are "strong views on all sides of the debate".
The document indicates Selmayr argued for a shorter Brexit delay than the three-month period now being suggested.
The draft paper obtained by the Financial Times said Britain has to take part in the May 23-26 votes if it wants an extension of more than three months.
Over the past week, a series of Brexit votes have taken place in the Commons.
In total 17 Labour MPs voted against the amendment, which was defeated by 334 votes to 85.
Originally, Corbyn had been against the idea of the second vote, yet with the abrupt exit of eight members of Labour, the leader favoured the referendum.
According to the minutes, the European commission's secretary general, Martin Selmayr, who is known as a master of strategy, asked: "Imagine that they have a new Brexit secretary or prime minister - what then?"
However, 24 Labour MPs rebelled to vote for the motion.
But if the Commons has not passed a resolution approving the negotiated withdrawal agreement by March 20, then the motion said it is "highly likely" the European Council would require a "clear goal for any extension" and to determine its length. Few opposition lawmakers backed the measure and even campaigners for a "people's vote" said the time was not yet right.