EU leaders meeting in Brussels on Wednesday must decide by unanimity on any further delay. British Prime Minister Theresa May asked the bloc on Friday for a second postponement until June 30, with the possibility of leaving earlier.
Tusk, who will chair the summit, has instead proposed a delay of up to one year, which could be cut short if the UK parliament approves an EU divorce deal. May is in talks with the opposition Labour party to try to get the votes.
"Discussion showed wide support for Tusk's idea of a long 'flextension'," the EU official said on condition of anonymity.
EU leaders only two weeks ago rejected a request from May for a reprieve until June 30 and several national diplomats said all options were still on the table - from refusing a further delay and heading towards a no-deal Brexit to granting May's request or pushing for a long postponement.
"We are waiting to see if there is any real progress with Labour. Depending on what May comes with on Wednesday, how much clarity there is on the UK side, we still have the three options," said another EU diplomat briefed on the meeting.
"Accepting her request is tough for some in the EU. June 30 is as tricky as it was two weeks ago because of the sensitivities around the European Parliament elections ... A long delay is a way of reducing uncertainty and avoiding constant emergency Brexit summits."
May has accepted that Britain will have to prepare to elect members of the European Parliament, but hopes to leave the bloc in time to pull out of polling.
As was the case two weeks ago, May will address the other 27 national EU leaders and answer their questions before leaving the room and letting them decide.
The last time, she left them with the sense that she did not control the situation or have a clear plan, hardening the line of EU states such as France that say Brexit uncertainty must end as soon as possible, even if this means an abrupt split.
"It is really a political decision for our leaders on the next steps from the EU side," said a senior EU diplomat who took part in the closed-door meeting.
EU diplomats stressed the need for "sincere cooperation" clauses in case of any long Brexit delay, to ensure Britain does not interfere unduly with the EU's reforms, its next budget, European Parliament elections or selecting the new executive Commission.
"For any kind of extension, the leaders want more clarification of the purpose ... If it is to hold another vote on the Withdrawal Agreement, this is clear. But if not, the leaders would want to know exactly what the reason would be," the senior diplomat said.
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