The European Parliament's lead negotiator on Brexit, Guy Verhofstadt, says the EU needs to have an agreement on UK withdrawal before the next European elections in May or June 2019.
In a tweet he said: "Brexit should be delivered before 2019, when EU politics enters into new cycle & the @Europarl_EN starts new mandate."
He will participate in the talks along with negotiators from the European Commission and the ministerial Council.
The talks are likely to start in 2017.
UK Prime Minister Theresa May says she will not trigger the Brexit mechanism - the EU's Article 50 - before next year, because detailed preparations are necessary.
Mr Verhofstadt, previously prime minister of Belgium, told journalists in Strasbourg that the European Parliament would "have to give consent to the agreement as stated in Article 50 so it's wise the parliament is involved from the start of this process.
"I want the UK to trigger Article 50 as soon as possible, so we can finalise these negotiations by 2019. I can't imagine we start the next legislative cycle without agreement over UK withdrawal."
Mr Verhofstadt is sympathetic to the Scottish government's case for keeping Scotland in the EU. Whereas 52% voted to leave the EU in the UK as a whole, in Scotland 62% voted to remain.
The UK is expected to have at least two sets of negotiations on Brexit - one to deal with the technicalities of withdrawal and another to cover the UK's future relations with the EU, including all-important trade ties. The latter is expected to take longer - some say it could take a decade.
The technicalities will need to address areas such as the UK's EU budget contributions and UK staff in EU institutions and projects.
Holding European elections in 2019 without a Brexit deal would be difficult, because 73 of the European Parliament's 751 MEPs represent the UK. After Brexit those seats will have to be axed or redistributed among the other 27 member states.
Free movement of people is expected to be a thorny issue, as the UK government has pledged to cut immigration from the EU.
Mr Verhofstadt, leader of the liberal ALDE group in Europe, said "the position of the parliament is very clear - if the UK wants to remain part of the single market, it'll have to accept the free movement of our citizens.
"In the opinion of parliament the four freedoms of the Union are inseparable."
The other three freedoms are: free movement of capital, services and goods.
The UK's Brexit Secretary, David Davis, was asked to respond during an appearance before MPs at Westminster.
"Mr Verhofstadt's comments are not new, he has been saying this for some time," he said.
Mr Davis said he would not be drawn into setting out the government's position, adding that "all these options are being kept open".