* Dollar index at strongest since late July
* U.S. Treasuries at 4-month highs
* Market awaits Fed minutes, Yellen speech this week
* Sterling slips again on Brexit worries
By Jemima Kelly
LONDON, Oct 11 (Reuters) - The dollar hit an 11-week high against a basket of major currencies on Tuesday as investors increased their bets on the U.S. Federal Reserve raising interest rates before the end of the year.
New Zealand's dollar was the biggest loser against the greenback, shedding as much as 1 percent to hit $0.7061 , its weakest since late July, after an official from the country's central bank reiterated that further rate cuts would be needed to jump-start inflation.
In contrast, traders have priced in a 70 percent chance the Fed will hike rates at its Dec. 13-14 meeting, up from 66 percent on Friday, according to CME Group's FedWatch tool. U.S. 10-year Treasury yields were trading at their highest in over four months.
Investors are looking to Wednesday's release of minutes of the latest Federal Reserve Open Market Committee meeting to see how close the Fed was to hiking rates last month.
Speaking to reporters after a speech in Sydney, Chicago Fed President Charles Evans said on Tuesday that he "could be fine" with the Fed raising rates in December, but he wanted to see how the economy and inflation progressed before deciding.
Some analysts said growing doubts over Donald Trump's ability to win the U.S. presidency were also helping to drive up the dollar, after the most senior Republican in Congress, Paul Ryan, distanced himself from him.
But not all agreed. "I think politics is difficult for the dollar these days - I don't know if the market has quite made up its mind about what to make of a possible Trump victory," said DZ Bank currency strategist Sonja Marten, from Frankfurt.
"I think (the dollar strength) is more to do with the Fed... At this point it seems like they're more willing to take a slightly more hawkish stance."
The dollar index climbed 0.3 percent to 97.251, its highest since late July.
Japanese, Canadian and some U.S. markets were closed on Monday for holidays.
Britain's beleaguered pound pushed lower again, falling 0.6 percent to $1.2281, well clear of the 31-year low of $1.1491 briefly touched during a "flash crash" on Friday, but leaving it down more than 4 percent since a week ago. On a trade-weighted basis, it hit an eight-year low.
"There appears to be little faith in sterling right now due to the huge uncertainties around Brexit, and therefore further turbulence likely lies ahead for the pound," said Oanda analyst Craig Erlam.
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 Tokyo markets team; Editing by Mark Trevelyan)