"The United Kingdom proposes that (the extension) should end on June 30 2019. If the parties are able to ratify before this date, the government proposes that the period should be terminated earlier," May wrote in a letter to EU Council president Donald Tusk, AFP reported.
May also told EU Council president Donald Tusk in a formal letter that Britain would start preparing for its participation in European Parliament elections in case it is still a member of the bloc when they begin on May 23.
"The United Kingdom proposes that (the extension) should end on June 30 2019. If the parties are able to ratify before this date, the government proposes that the period should be terminated earlier," May's letter said.
Downing Street released May's request moments after a senior EU official told AFP that Tusk was proposing to postpone Brexit day by up to a year, also pending parliament's approval of the EU-UK Withdrawal Agreement.
The current deadline is April 12, which has already been pushed back once from March 29 because of the UK Parliament's failure on three occasions to back the deal May signed with the other 27 EU leaders in December.
In her letter, May said she wanted to make sure that Britain left the bloc after 46 years in an orderly manner, with an agreement that could help unwind intricate political, security, diplomatic and economic ties.
"The government's policy has always been and remains to leave the European Union in an orderly way, and without undue delay," May wrote.
"The government agrees that leaving with a deal is the best outcome," she said.
May is racing against the clock in a desperate bid to get her deal approved in time for an EU leaders' summit in Brussels on Wednesday, when a formal decision on any extension will be made.
EU nations must give unanimous backing to any new deadline.
Some, like French President Emmanuel Macron, have said they want to hear a clear reason from May as to why Brexit should be delayed yet again – a move that would add to uncertainties weighing on business across the bloc.
May's team is currently holding negotiations with leaders from Britain's main opposition Labour Party in a bid to secure enough votes to push through her deal on a fourth attempt.
But the talks so far have failed to clinch a breakthrough.
"I don't think we are quite at the point where the government can indicate where their concessionary strategy might apply," deputy Labour leader Tom Watson told BBC radio.