"The UK should trigger the Article 50 as soon as possible so that we can finalize these negotiations by 2019," Verhofstadt was quoted as saying by the EU Observer newspaper.
According to the paper, Verhofstadt said that a new EP legislative cycle should not start without an agreement on the issue. The next EP elections are set to be held in 2019.
On June 23, the United Kingdom held a referendum to determine whether or not the country should leave the European Union. According to the final results, 51.9 percent of voters, or 17.4 million people, decided to support Brexit, while about 16.1 million opposed it.
UK Prime Minister Theresa May has repeatedly said she would not trigger the Article 50 of the EU Lisbon Treaty on leaving the bloc until early 2017.