Two EU officials said a Bloomberg report of an imminent Brexit deal was "premature". However, a third official said there had been some "serious convergence of views" in technical talks while chief EU negotiator Michel Barnier and other senior officials said progress was being made.
Any new deal will still have to go to a fractious British parliament which rejected several attempts by Prime Minister Boris Johnson's predecessor Theresa May to push through the withdrawal agreement she agreed with Brussels.
"There are indications that this could be a more palatable option compared to May's deal which has been rejected thrice previously," said Andrea Cicione, head of strategy at TS Lombard. "That's clearly a good development."
With the pound surging on the positive noise around Brexit, internationally-focused firms on London's blue chip FTSE 100 came under pressure, while the domestically-focused midcap index climbed 1.3%.
British banks Lloyds, Royal Bank of Scotland and Barclays, considered some of the most vulnerable to the UK economy and Brexit uncertainty, rose between 4% and 5%.
The pan European STOXX 600 index jumped 1.1%, with other major regional indices including Germany's DAX and France's CAC 40 gaining a similar amount.
Also boosting sentiment was an upbeat start to the US quarterly earnings season with better than expected reports from J.P. Morgan and Johnson & Johnson.
"The kick off of reporting season could support today's sentiment as markets try to cross-read some positive numbers coming from the United States," said Societe Generale European equity strategist Roland Kaloyan.
Europe's bank index rose 2.5%, leading gains among the major sectors, while retailers gained 2.4%.
Recruiter Hays Plc jumped 8.1% after it reported steady first-quarter net fees due to strong hiring in the United States and China.
Shares in Wirecard, however, slumped 12.8% after the Financial Times published documents on the company's accounting practices alleging an effort to inflate sales and profits, dealers said.
Dutch semiconductor equipment maker ASML gained 3% after reports that South Korea's Samsung has agreed to buy high-end lithography machines from the company.
German meal-kit company Hellofresh rose 23.4% after the company raised its full year forecast, hauling Germany's small-cap index 1.7% higher.