* Graphic: World FX rates in 2020 http://tmsnrt.rs/2egbfVh

* Graphic: Trade-weighted sterling since Brexit vote http://tmsnrt.rs/2hwV9Hv

LONDON, July 30 (Reuters) - Sterling hovered close to one-month highs on Friday and was on course for its strongest week since December ahead of a Bank of England meeting next week.

A drop in COVID-19 cases, although they are still high, and the reopening of the British economy have fuelled a rebound in the pound -- it has added nearly 3% in less than a fortnight to hit close to $1.40.

Broad dollar weakness, which was exacerbated by a dovish Federal Reserve meeting this week, has also helped sterling.

At 1400 GMT, the pound was little changed at $1.3956 , near the one-month high of $1.3983 reached on Thursday.

The pound has gained around 1.4% against the dollar this week -- making it one of the top performing major currencies.

Against the euro, sterling was a little weaker at 85.19 pence, although it remains close to its strongest level versus the single currency since early April.

The BoE, which meets on Thursday, is expected to keep its foot firmly pressed on the stimulus pedal. But there is growing discussion about the need to begin tapering its bond-buying programme as the economy recovers. Two BoE policymakers have said the time for tighter policy may be nearing amid rising inflationary pressures.

"Markets appear to be rebuilding some GBP long positions ahead of next week’s Bank of England meeting, with sentiment on the currency that has recently been buoyed by a contraction in COVID-19 cases in the UK despite most restrictions having now been lifted," ING analysts said in a research note.

(Reporting by Tommy Wilkes; editing by Barbara Lewis and Clelia Oziel)