U.K. Prime Minister Theresa May attempted to accelerate Thursday, but her European counterparts want to know how much London will pay to exit the bloc.

May wrote a letter, published Thursday morning, reassuring all European citizens living legally in the U.K. that they can remain.

"I couldn't be clearer: EU citizens living lawfully in the U.K. today will be able to stay," she wrote. "But this agreement will not only provide certainty about residence, but also healthcare, pensions and other benefits."

Though her words were welcomed in Brussels, European officials said that without a proposal and agreement on budgetary commitments by mid-December, there will be a hard Brexit — meaning that after March 2019, the EU and the U.K. would be trading under World Trade Organization rules with higher costs for businesses.

"Without budget agreements, we can't reach a deal before December and then everything derails and we head towards a hard Brexit," a EU official, who didn't want to be named due to the sensitivity of the talks, told CNBC Wednesday.