UPDATE 1-Deal or no deal? Sterling slips as traders eye Brexit summit

* Graphic: sterling and gilt yields http://bit.ly/2dgAXn1

* Graphic: World FX rates in 2017 http://tmsnrt.rs/2egbfVh

* Graphic: Trade-weighted sterling since Brexit vote http://tmsnrt.rs/2hwV9Hv (Adds quotes, details, updates prices after construction PMI)

LONDON, Dec 4 (Reuters) - Sterling slipped against a stronger dollar on Monday, as investors awaited the outcome of a summit in Brussels where British Prime Minister Theresa May hopes to break a deadlock in Brexit talks with a new divorce offer.

Better-than-expected economic data showing a modest rebound in British construction activity last month had little perceptible impact on the pound, with the Brussels talks stealing the limelight in London trading.

Sterling edged 0.4 percent down on the day to $1.3431 , having touched a two-month high of $1.3550 last week.

Over lunch later on Monday with European Commission President Jean-Claude Juncker and European Union Brexit negotiator Michel Barnier, May will try to persuade them to start discussions on a new trade pact and a two-year transitional deal.

London has broadly agreed to many of the EU's divorce terms, including paying out something like 50 billion euros. But the issues of the rights of expatriate citizens and the UK-EU border on the island of Ireland remain fraught, diplomats said.

"If a green light is provided today for talks to move on to future relations, including a timely transition arrangement, it would open the door for further pound gains in the near-term," said MUFG currency economist Lee Hardman.

"In contrast, the pound could weaken sharply if the EU still refuses to judge that sufficient progress has been made on divorce talks. (That) would increase the risk that Brexit talks will break down, and make a more disorderly Brexit outcome more likely."

A Reuters poll last week found economists believe the chance of such a "disorderly Brexit" - where no deal has been reached when the two years of talks are scheduled to close in March 2019 - has declined over the past month.

Such optimism drove sterling to six-month highs on a trade-weighted basis last week, and it traded around 0.4 percent below those highs on Monday.

Against the euro, the pound was 0.1 percent up on the day at 88.26 pence.

Speculators bought back into the pound in the week up to last Tuesday, data showed on Friday, with positioning moving into positive territory - reflecting more bets that sterling will strengthen than that it will fall - for the first time since October.

"Strong signals could emerge later today as to whether EU negotiators are recommending to EU leaders that Brexit negotiations should move to Phase II," said ING currency strategist Chris Turner. (Editing by Peter Graff)