U.K. financial services firms will definitely not be able to carry on business as normal within the European Union (EU) after it leaves the bloc, according to Luc Frieden, who has held several portfolios within the Luxembourg cabinet over the past few decades.

"We need a strong partnership with the United Kingdom, it's our neighbor and it's going to remain an important financial services center. Yet at the same time, 'out' is not 'in' and therefore I think the United Kingdom must know that it's not going to benefit anymore over the passporting rights it used to have," Luc Frieden told CNBC on Friday in Luxembourg.

"So with those two pillars, I think in between a deal can be found but it will be very difficult and it will take a lot of time," he added, noting that he anticipated the just over 18 months remaining on the timeline was wholly unrealistic.

So-called passporting rights allow financial services firms within the EU to run operations and offer services throughout the European Economic Area (which consists of the EU member states as well as Norway, Iceland and Lichtenstein). Given the U.K. economy's weighty dependence on financial services, the question of the country's ability to hold onto these rights once it has left the trading bloc has been flagged as a key discussion topic for exit negotiations.