The UK is currently due to leave the EU on April 12 and no withdrawal deal has been approved by MPs yet.
May said she wanted an extension to June 30 -- a date rejected by the European Union when the UK last sought a delay -- to give more time for cross-party negotiations over the political impasse in London.
However, it is likely that the EU will propose a longer process instead. Tusk is understood to prefer a year-long extension, which could be shortened if and when the UK ratifies a withdrawal deal, the BBC reported.
It is not clear, however, if Tusk plan will will be favoured by all EU member states. The diplomat said that "some ritual rumbling" could be expected, reports say.
May said a further postponement to the Brexit date is needed if the UK is to avoid leaving the EU without a deal, a scenario both EU leaders and many British MPs believe would create problems for businesses and cause difficulties at ports.
In any event, the UK must start preparing for elections to the European Parliament, which begin on May 23.
May wrote in her letter that the UK government "accepts the European Council's view" that it would be under a "legal obligation" to hold European Parliament elections. The elections would be cancelled if a deal is reached before them, she said.
The Prime Minister May said it was "frustrating that we have not yet brought this process to a successful and orderly conclusion," adding that the UK government "remains strongly committed to doing so and will continue to act as a constructive and responsible member state of the European Union in according with the duty of sincere cooperation throughout this unique period".
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)