May said that if an agreement was reached before this date, the UK proposed that the extension should be ended early.
She has proposed that if UK MPs approve a deal in time, the UK should be able to leave before European Parliamentary elections on 23-26 May.
But she said the UK would prepare to field candidates in the EU-wide elections in case no agreement is reached.
EU leaders, who meet in Brussels on Wednesday to discuss the Brexit deadlock, must agree unanimously whether to grant an extension to the Article 50 process, under which the UK leaves the EU.
This comes after UK MPs repeatedly rejected the Withdrawal Agreement reached between the UK and the bloc.
The letter, sent today, reads, “The Government will want to agree a timetable for ratification that allows the United Kingdom to withdraw from the European Union before 23 May 2019 and therefore cancel the European Parliament elections.”
Meanwhile, it is believed that Tusk has suggested a year-long Brexit delay, adding that this would allow the UK to leave on July 1 in the event that its Parliament has ratified the EU divorce deal by then.
“The Government will want to agree a timetable for ratification that allows the United Kingdom to withdraw from the European Union before 23 May 2019 and therefore cancel the European Parliament elections” Theresa May’s letter to the EU
It is not known, however, how Tusk’s proposal could be reconciled with May’s request for a second Brexit postponement until June 30.
A senior EU official was quoted on Friday saying, “Flextension allows for leaving the EU on July 1 as well. Only that they would have to finalise the ratification of the Withdrawal Agreement by then.”
The search for a Brexit breakthrough has moved to a different phase, with talks between May and UK Labour leader Jeremy Corbyn.
The first exchanges were said to be 'constructive' and they agreed a 'programme of work' to try to find a way forward.
Further discussions are planned for later today.
Meanwhile, German Chancellor Angela Merkel has said Germany will stand with Ireland "every step of the way" over Brexit.
She was speaking following talks in Dublin with the Taoiseach about the current deadlock.
Merkel was asked if it was possible to protect the integrity of the single market without an Irish border being in place.
She said: "We will simply have to be able to do this. We hope for a solution we can agree together with Britain.”