Brexit talks are set to miss their first big deadline

European leaders were set to give the greenlight to start trade talks with the U.K. next week but now this might not happen until December, officials and analysts have told CNBC.

A lack of progress in the negotiations is increasing the uncertainty for businesses and citizens, who both need to cement their post Brexit-plans as soon as possible.

"I fear all this is too little for Michel Barnier (the European negotiator) to ask the EU leaders to give him a green light to open up negotiations about the future," Agata Gostynska-Jakubowska, research fellow at the Centre for European Reform, told CNBC via email.

"He is a serious statesman — he will not make any recommendations concerning sufficient progress until he is perfectly certain that he has found common ground with the U.K," she added.

Negotiators have repeatedly failed to agree on the terms of the Brexit bill, citizens' rights and the Irish border. The EU has ruled out discussing trade with the U.K. unless these points are satisfied.

"With every week that goes by without real progress — for instance, on a transition period — anxiety among businesses and markets will increase," Rem Korteweg, head of the Europe in the World unit at Clingendael Institute in the Netherlands, told CNBC.

"This will raise pressure on the U.K. government to compromise on, for instance, the Brexit bill. This could offer the breakthrough needed to move the talks to 'phase 2' (trade) by December. But there is little certainty this will indeed happen," he said.

European Council President Donald Tusk said Tuesday that he hopes trade talks will begin before the end of the year; if not, both negotiating teams will have to change their approach to negotiations.

"We are negotiating in good faith, and we still hope that the so-called 'sufficient progress' will be possible by December. However, if it turns out that the talks continue at a slow pace, and that sufficient progress hasn't been reached, then — together with our U.K. friends — we will have to think about where we are heading," Tusk said.

Some analysts predict that a breakthrough will be made on the three key issues by the end of the year. But doubts remain whether that will be enough to conclude Brexit talks in time for approval at the European Parliament before March 29, 2019 – the date the U.K. is set to leave the European Union.

British Prime Minister Theresa May has said that both sides will have to agree an additional transition deal to ensure that businesses and citizens won't be faced with an abrupt change on March 29, but that also requires time.

"There will be no real change in negotiations until December at the earliest, which makes timing increasingly tight for any exit agreement or transitional arrangements to be settled," Andrew Hood, former legal advisor to David Cameron and senior director of Dechert LLP, told CNBC.

Media reports suggest that the U.K. government is making precautionary plans in case it doesn't reach any agreements with the EU.

Tusk said Tuesday the EU isn't working on such a scenario. "We hear from London that the U.K. government is preparing for a "no deal" scenario," he said. "I would like to say very clearly that the EU is not working on such a scenario."

Meanwhile, recruiters are using Brexit to attract highly-skilled and young professionals back to their home countries.

"Brexit is a moment at which many are thinking of returning, so we want to encourage them to return home," Ivan Jimenez, the managing director of Bizkaia Talent, a non-profit organization that supports people interested in being relocated to the Basque country in northern Spain, told CNBC via email.

The autonomous region lost many highly-educated people during the last financial crisis and currently faces a shortage of talent, including in engineering, academia and the financial services. However, it's also a question of demographics given the Basque country has one of the oldest populations in Europe.

"It is not just financial services and automotive, it is engineering and also academia, where there are real concerns amongst Basque academics living in the U.K. that the U.K. will lose research funding after leaving the EU and therefore their jobs are at risk," Jimenez said.