(Updates prices, adds comment)

* Dollar falls 0.8 pct vs yen as U.S. yields, shares fall

* Sterling hits more than two-month lows vs dollar

* Weekend comments from British PM suggest hard Brexit

* Dollar dips vs euro, franc

By Sam Forgione

NEW YORK, Jan 9 (Reuters) - The U.S. dollar slumped against the safe-haven yen on Monday on investors' reduced appetite for risk, while sterling sank to more than two-month lows on talk that Britain would drastically rework trade ties with the European Union after Brexit.

A fall in U.S. Treasury yields and stocks drove the dollar down as much as 0.8 percent against the yen to a session low of 115.97 yen. The dollar remained within recent trading ranges and did not test Friday's more than three-week low of 115.04 yen.

Analysts said there was no fundamental catalyst for the dollar's decline against the yen, with traders probably reacting to lower U.S. yields and equities.

"There's an optical relationship with the fact that stocks are lower," said Shahab Jalinoos, global head of FX strategy at Credit Suisse in New York.

The dollar also fell against the euro and Swiss franc, leading the dollar index, which measures the greenback against a basket of six major currencies, 0.26 percent lower at 101.950.

The pound slid more than 1 percent against both the dollar and the euro after weekend comments from British Prime Minister Theresa May that she was not interested in keeping "bits of membership" of the European Union.

Sterling slid as low as $1.2125, its weakest against the dollar since the end of October. It fell about 1.3 percent against the euro, hitting 86.99 pence per euro, the lowest since mid-November.

The euro's strength against the pound had a knock-on effect of pushing the euro higher against the dollar, said Richard Scalone, co-head of foreign exchange at TJM Brokerage in Chicago.

"The reason why the euro has been relatively well-bid is because a lot of people trade euro/sterling," he said. Analysts also said that some strong European data, including figures showing German exports rose 3.9 percent in November to mark their strongest monthly gain since May 2012, supported the euro against the dollar.

Against the dollar, sterling was last down 1 percent at $1.2161, while the euro was up 0.4 percent against the dollar at $1.0567. The dollar was down 0.3 percent against the franc at 1.0148 francs.

On Wall Street, the benchmark S&P 500 stock index was down 0.23 percent, while benchmark 10-year U.S. Treasury yields were last down about four basis points at 2.376 percent.

(Reporting by Sam Forgione; Additional reporting by Marc Jones in London; Editing by Lisa Von Ahn and Meredith Mazzilli)