Barnier, the EU's chief negotiator, told a forum in Slovenia that it was "realistic" to expect a divorce deal with Britain, the British embassy to Slovenia said on Twitter.
For a market broadly short the pound because of worries that Britain will crash out of the trading bloc next year without any sort of formal trading arrangement, that signaled the UK can avoid a disorderly no-deal Brexit.
The British currency rallied across the board, rising more than one percent to $1.3052, its highest level in five weeks.
The pound also rose to a one-month high against the euro at 88.96 pence while versus the Swiss franc it was headed for its biggest one-day rise in more than 18 months.
"It just shows that's the key thing that people want to see -- Brexit progress. You have a market that's heavily short on sterling due to Brexit. It needs that tail risk to be taken off before sterling can rally," said Viraj Patel, a currency strategist at ING in London.
Before Barnier's comments, the pound had traded modestly higher against the dollar and euro as data showed the British economy posting its fastest growth in almost a year.
Data showed British gross domestic product in the three months to July was 0.6 percent higher than in the previous three-month period, gathering pace from 0.4 percent growth in the three months to June, and at the top end of forecasts.
Sterling has rallied in recent weeks off lows below $1.27, lifted by earlier seemingly favourable comments from Barnier.
On Friday he was quoted as saying the EU was open to discussing other "backstops" on Brexit, especially the Irish border issue, a key hurdle to agreeing a deal.
"Any scope for a deal to be achieved, particularly coming from one of the chief negotiators is a bullish signal," said Craig Erlam, market analyst at OANDA.