* Dollar climbs against yen, steady against euro
* Sterling drops around 1 percent in reaction to PM Brexit comment
* Graphic: World FX rates in 2016 tmsnrt.rs/2egbfVh
By Marc Jones
LONDON, Jan 9 (Reuters) - Talk of Britain dramatically reworking trade ties with the European Union after Brexit sent the pound tumbling to two-month lows on Monday, as signals the United States could raise interest rates three times this year lifted the dollar.
The pound slid around 1 percent against both the dollar and the euro in early trading after weekend comments from British Prime Minister Theresa May that she was not interested in keeping "bits of membership" of the European Union.
May said she instead wanted a bespoke deal and also denied criticism that she was "muddled" in the pursuit of what she called the right relationship with the EU, the country's largest trading partner.
Sterling fell 0.9 percent to as low as $1.2164, its weakest against the dollar since the end of October. It fell 1.1 percent against the euro too, hitting 86.65 pence per euro, the lowest since mid-November.
"The most significant thing is May's comments over the weekend (on a Brexit deal) triggering a significant sterling slide," said Saxo bank's head of FX strategy John Hardy.
"My feeling is we kind of knew this so what did the market expect really, but her making it explicit gives another reason to short sterling maybe."
The dollar, meanwhile, crept ahead after signs of wage pressure in the December U.S. jobs report on Friday proved enough to lift key 10-year Treasury yields from 2.33 percent to 2.42 percent after a sizable fall earlier in the week.
Chicago Federal Reserve President Charles Evans added following the jobs numbers that the central bank could raise interest rates three times this year, faster than he had expected just a few months ago.
The euro edged up 0.2 percent to $1.0550, as the steepest monthly rise in German exports in four-and-half years helped the bolster the shared currency which had ricocheted between $1.0339 and $1.0621 last week.
"The New Year started with some mildly good news," ING economist Carsten Brzeski said, adding that the latest batch of figures brought evidence that the economy gained momentum in the final quarter of the year.
Cross-asset traders though are still focusing primarily on the dollar and whether the reflation theme, that finally took a firm hold after Donald Trump's November election win, is priced in sufficiently.
Two non-voting Fed presidents will speak later on Monday, and there are no less than five speeches lined up for Thursday. The main economic release of the week is not until Friday, when retail sales figures for December are out.
Dealers in Asia will also be keeping a wary eye on the yuan after Beijing engineered a sharp tightening in liquidity last week that squeezed speculators out of short yuan/long U.S. dollar positions.
China's central bank kept up the pressure on Monday, setting a firmer fix for the yuan than many had expected at 6.9262 per dollar, even though that was down from the previous fix.
Yet the defence is proving costly.
Figures out over the weekend showed China's foreign exchange reserves fell to nearly six-year lows in December as Beijing fought to stem an outflow of capital that could ultimately force another devaluation of the currency.
For Reuters new Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.biz/cms/?pageId=livemarkets
Additional reporting by Wayne Cole in Sydney; Editing by Toby Chopra