Hopes are building that a Brexit deal can be reached before an EU summit on Oct. 18.
European Union Brexit negotiator Michel Barnier said on Wednesday that 80-85 percent of the withdrawal deal was agreed and sterling rose as some investors unwound short bets on the currency.
But sterling on Thursday traded flat against the dollar at $1.3192, close to a 3-1/2 month high of $1.3244. It fell 0.3 percent versus the euro to 87.29 pence.
Barnier said Britain must accept possible checks on goods moving between its mainland and its province of Northern Ireland.
But the Northern Irish party that British Prime Minister Theresa May's government relies on for support has threatened to challenge her leadership if their wishes aren't respected on the Irish border.
"Building optimism over a potential breakthrough in Brexit talks at next week's summit is continuing to encourage pound outperformance," said analysts at MUFG.
The analysts said that if a no-deal exit from the bloc was avoided the currency could strengthen by a further 5-10 percent in the coming months.
May will update some senior British ministers on Thursday on the progress of Brexit negotiations brief her cabinet on Tuesday before she heads to Brussels for the EU summit.