A JPMorgan index that tracks domestically-focused UK stocks was headed for its best day since it was created in 2017, while Ireland's main stock index added 2.7pc and was on track for its biggest one-day percentage gain this year.
German shares eyed their best day in four months, also helped by gains for SAP, Europe's most valuable technology company, after its long-term CEO stepped down.
The chief Brexit negotiators of the EU and Britain met on Friday, hours after Prime Minister Boris Johnson and his Irish counterpart unexpectedly said they had found a pathway to a possible deal at last-ditch talks.
Investment bank JPMorgan said it now saw a 50pc chance of a withdrawal agreement being struck with a "modified/time-limited" Irish backstop. It had previously put the likelihood at just 5pc.
"The psychological take on it for markets is that there is a real hunger to see some sort of breakthrough, even if it's just a small one that can be built on," said Ken Odeluga, market analyst at City Index.
"But on the other hand, there's not a great deal of evidence yet that a breakthrough has truly arrived."
London's exporter-heavy FTSE 100 index erased early losses to trade up 0.2pc, with stocks such as homebuilders and UK-focussed banks with the greatest sensitivity to Brexit updates among the biggest gainers.
Signs of an imminent divorce deal after three years of chaotic negotiations were enough to push London-listed companies with exposure to the domestic economy to a premium over the blue-chip index for the first time since May.
The pan-European STOXX 600 climbed 1.3pc and was headed for its best week in nearly two months, with rising hopes for at least a partial US-China trade deal adding to investor sentiment.
US Treasury Secretary Steven Mnuchin, Chinese Vice Premier Liu He and other senior officials will resume discussions on Friday.
Germany's SAP rose 7.7pc to its highest level in more than two months after it released a strong set of third-quarter results and said CEO Bill McDermott was stepping down after a decade at the helm.
Publicis tumbled 14.2pc to a seven-year low after the ad firm lowered its full-year sales target for the second time in 2019. Its London rival WPP lost 4.4pc.
Fashion house Hugo Boss sank 13pc to its lowest in almost a decade after the company cut its 2019, earnings forecast and reported third quarter results below expectations.
Those numbers came hard on the heels of a strong sales update from Louis Vuitton owner LVMH on Thursday.