• "There is a path to an agreement now," European Commission President Ursula von der Leyen said Wednesday.
• Sterling and the euro climbed versus the dollar following her comments, trading at $1.35 and $1.22, respectively.
• Business activity in the euro zone is having a fairly robust December, according to the latest PMI data for the region.

LONDON — European stocks closed higher on Wednesday as the EU signaled progress in talks over a post-Brexit trade agreement with the U.K.

The pan-European Stoxx 600 closed up by 0.8%, with almost all sectors bar banks in positive territory. Insurance shares led the gains, climbing 2.1%.

"There is a path to an agreement now," European Commission President Ursula von der Leyen said Wednesday, in comments that boosted sterling and the euro. Both currencies climbed versus the dollar, trading at $1.35 and $1.22, respectively.

"We have found a way forward on most issues but two issues remain outstanding: the level playing field and fisheries," von der Leyen said.

On Wall Street, stocks hovered around the flatline as traders weighed apparent progress in U.S. fiscal stimulus talks and disappointing economic data.

The Commerce Department said retail sales fell by 1.1% in November. Economists polled by Dow Jones expected a decline of 0.3%.

Global investors also looked ahead to the Federal Reserve's comments regarding the future of the U.S. economy.

While the Fed's long-term view is expected to be improved due to vaccine optimism, the central bank is expected to sound very dovish at the end of its meeting.

Back in Europe, the surge in coronavirus cases is also a key focus for investors with several major economies, including Germany, Italy and the Netherlands, changing Christmas plans to relax restrictions in order to curb a sharp rise in cases.

On Wednesday, Germany is starting its Christmas lockdown in which schools and nonessential shops must close. The U.K. too is reconsidering plans to relax rules to allow families to gather over the festive period after high-profile criticism of the move.

Robust euro zone data

Business activity in the euro zone is having a fairly robust December, according to the latest preliminary purchasing manager's index (PMI) data for the region.

The flash euro zone PMI composite output reading, which looks at activity in both manufacturing and services sectors, came in at 49.8 in December, up from 45.3 in November and beating expectations. A reading below 50 still indicates a contraction in business activity, however.

In terms of individual share price movement, telecoms and cable group Altice Europe soared more than 23% after its founder increased a buyout offer to take the company private.

At the bottom of the European blue chip index, shares of Belgian pharmaceutical company Galapagos plunged more than 18% after U.S. partner Gilead opted not to seek approval for a rheumatoid arthritis drug, according to Reuters.

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- CNBC.com staff contributed to this market report.