European Council president Donald Tusk has said a "short extension" to Article 50 should be possible "conditional" upon a positive vote in the UK parliament.
Mr Tusk, speaking in Brussels, said: "In the light of the consultations that I have conducted over the past days, I believe that a short extension would be possible.
"But it would be conditional on a positive vote on the Withdrawal Agreement in the House of Commons.
"The question remains open as to the duration of such an extension."
Earlier today Mrs May requested a three-month delay to Brexit, postponing the UK's departure from the European Union from March 29 to June 30.
Mr Tusk added: "At this time, I do not foresee an extraordinary European Council.
"If the leaders approve my recommendations and there is a positive vote in the House of Commons next week, we can finalise and formalise the decision on extension in the written procedure.
"However, if there is such a need, I will not hesitate to invite the members of the European Council for a meeting to Brussels next week."
Mr Tusk added: "Although Brexit fatigue is increasingly visible and justified, we cannot give up seeking until the very last moment a positive solution - of course, without opening up the Withdrawal Agreement.
"We have reacted with patience and goodwill to numerous turns of events and I am confident that also now we will not lack the same patience and goodwill at this most critical point in this process."
Earlier this week House of Commons Speaker John Bercow ruled that the British prime minister cannot bring her EU withdrawal deal back before MPs unless it is substantially different from the package which was decisively defeated last week.
