A planned £367million (€420million) rebuild of the site which is only 25 years old would also make improvements to other services such as catering.
If the rebuild deal is finalised before the end of the Brexit transition period at the end of 2020, then Britain is likely to be lumbered with a bill of around £47million.
One of the key selling points of the new design is the way in which it would separate MEPs from the general public.
A report into the rebuild suggests politicians have apparently become uncomfortable with the way the public can access the site.
The current building was designed in the 1980s when the “context regarding security” was different, according to the report.
It is “far from ideal” that MEPs can “still accidentally mix with other flows” of people, including “visitors, press, and maintenance personnel”, it reads.
A final decision on the rebuild has been postponed until after next year’s European elections.
The building, completed in 1993, cost more than £875million (€1billion).
More than £1.75billion (€2billion) has been spent on EU buildings in Brussels and the other seat in Strasbourg since the 1990s.
One Conservative MEP said the rebuild should mean the EU only use one of their parliamentary seats to recoup costs.
Ashley Fox, leader of the Tory MEPs said the EU should stop “shuttling” between Brussels and Strasbourg.
He said: “At the very least there should be a guarantee that the new or refurbished building will last longer than the current one.
“I suggest taxpayers are promised that the new building will become the Parliament’s single seat.
“The savings generated by not shuttling to and from Strasbourg would recoup the cost of even a full €380 million (£332million) rebuild within four years.