Britain's Union Jack national flag is pictured during a debate on Britains withdrawal from the EU during a plenary session at the European Parliament on January 16, 2018 in Strasbourg.

Extending the official Brexit deadline for the U.K. could bring a wave of extra logistical and political problems for the European Union.

The ongoing deadlock has sparked a debate on the potential extension of Article 50 — the legal means by which the U.K. leaves the EU. However, there is strong opposition from some European lawmakers over giving more time to the U.K. to sort out its domestic politics.

The U.K. is set to leave the EU on March 29 — but this could change if the U.K. asks for an extension and the other 27 member nations accept the request. Extending the departure beyond the agreed date would likely clash with European parliamentary elections that are set to take place between May 23 and 26. The chamber is made of lawmakers from all 28 European member countries, including the U.K., and is responsible for approving European policies, such as the Union's total budget.

"What we will not let happen, deal or no deal, is that the mess in British politics is again imported into European politics. While we understand the U.K. could need more time, for us it is unthinkable that Article 50 is prolonged beyond the European Elections," Guy Verhofstadt, a member of the European Parliament and its representative in Brexit negotiations, said on Twitter on Wednesday.

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His comments come at a time when U.K. Prime Minister Theresa May's proposed Brexit deal suffered a historic defeat in the House of Commons on Tuesday. Meanwhile, French President Emmanuel Macron weighed in on the possibility that the U.K. would have to push back its departure date.

Macron said Wednesday that the U.K. "will take more time (to overcome the Brexit impasse), maybe they will step over the European elections in order to find something else."

Speaking to CNBC via email Friday, Seb Dance, member of the European Parliament for the U.K. Labour party, said the prospect of having Brexit and the European elections clashing "is a logistical headache."

"The impact of delaying Brexit on the EU elections is certainly troublesome logistically speaking," he said, "but politically speaking it shouldn't make a difference as it is entirely possible that elections take place in the other member states without needing to take place in Britain."

However, some argue that even politically, it would be troublesome, as European officials and institutions want to focus on campaigning and speaking to voters ahead of the vote. The wave of populist sentiment in Europe after the fallout of the sovereign debt crisis has raised concerns, among the traditional parties, about what the next European Parliament will look like.

According to a Brussels-based European official, who did not want to be named due to the sensitivity surrounding the Brexit talks, an extension would likely mean that the U.K. would have to participate in the vote. This is because it would still technically be a member of the European Union.