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Sterling hovers below $1.36 as investors await May's Brexit speech

* 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

LONDON, Sept 22 (Reuters) - Sterling traded within a tight range against the dollar on Friday while investors waited for a speech by British Prime Minister Theresa May in which she is expected to try to rescue stalled Brexit talks.

Investors will watch to see if May can offer enough to European Union negotiators to persuade them to move talks forward, without angering eurosceptic members of parliament who have the power to destabilise her government.

One of the issues May is expected to address in her afternoon speech in the Italian city of Florence is Britain's exit bill, which Brussels has demanded progress on before talks can progress.

Britain has expressed frustration at the European Union's demands, with British ministers keen to start negotiating the terms of Britain's new relationship with the bloc. Brussels has recoiled at Britain's approach, criticising a lack of detail and policy direction.

Sterling had risen against the dollar on Thursday after the BBC reported May will say Britain is willing to pay 20 billion euros ($24 billion) to the EU during a post-Brexit transition period, but only if it has access to the bloc's single market.

In morning trade in London, the pound was flat at $1.3581 , trading in a tight range of between $1.3595 and 1.3565.

Against a broadly stronger euro, it was around half a percent lower at 88.33 pence.

"The temptation is to say that because much of the content of the speech has been widely reported on already, that the impact on the currency will be small," Sam Lynton-Brown, currency strategist at BNP Paribas, said.

"However, FX options markets are pricing in quite a premium for the moves in the currency today and previously we've seen sterling be quite sensitive to speeches from Theresa May."

The pound has risen over 5 percent against the dollar this month, most of its gains coming largely on the back of a hawkish shift in the Bank of England's stance on record low UK interest rates. At its latest policy meeting, the BoE said interest rates could rise in "coming months", prompting many banks, including Nomura, to forecast a hike as soon as November.

"We think the likelihood of the MPC (BoE's monetary policy committee) not moving in November is slim," they wrote in a note to clients.

Investors were also watching out for a sovereign debt rating of Britain from credit ratings agency Moody's due later in the day.

(Reporting by Ritvik Carvalho. Editing by Jane Merriman)