Talks between May's top government lawyer and European Union negotiators to win concessions from the bloc on Brexit ended on Tuesday without agreement and no breakthrough is expected before the weekend.
Britain is due to leave the EU in 23 days and sterling investors are on edge. The pound has dropped this week as doubts mount over how, or possibly even if, Britain's exit will take place.
A Reuters poll found that most economists thought Brexit would be delayed by a few months and the two sides will eventually agree a free-trade deal.
May has offered lawmakers the chance to seek to prevent a no-deal departure and to delay Brexit if parliament rejects the deal in a vote she has promised to hold by March 12.
"If the EU does not make further concessions the vote next week - which could be delayed - is probably doomed to fail," said Esther Maria Reichelt, an FX strategist at Commerzbank in Frankfurt.
"Even if a no-deal Brexit is taken off the agenda next week, the uncertainty of what would happen in case of a postponement remains. Pound traders cannot ignore this fact ... things remain tense for sterling," she added.
At 0930 GMT the pound was down 0.3 percent at $1.3140, close to a one-week low of $1.3097 hit on Tuesday. It was also struggling against the euro, down 0.2 percent at 86.02 pence.
There was little obvious reaction in the pound to reports that Britain is considering dropping some tariffs in the event of a no-deal Brexit, "probably down to the fact that markets still consider it a remote possibility at this stage" said CMC Markets' Michael Hewson.
One of the best-performing major currencies so far in 2019, sterling rose sharply last week as investors bet a no-deal Brexit would be avoided and Britain's EU exit delayed.