* Russian shares dive more than 4%

* MSCI slips, eyes biggest one-day drop in a month

* U.S., Britain order Kyiv embassy departures

* Alibaba slides more than 6%

Jan 24 (Reuters) - Emerging market shares fell sharply on Monday in anticipation of a hawkish U.S. Federal Reserve this week, while Russia's volatile rouble steadied at nine-month lows with the West growing increasingly anxious of a possible Ukraine invasion.

After ending last week down 1%, MSCI's index of emerging market shares slid another 1.2% on Monday, on course for its steepest one-day drop in a month.

Some analysts are starting to speculate that, though unlikely, the Fed may hike rates this week as inflation surges. Most investors have priced in a 0.25% hike in March and three more by year end.

Indian shares led losses in Asia, falling more than 2%, while Russian shares sank more than 4%.

Russia's rouble, which marked its biggest weekly drop in two months on Friday, firmed up to 1% before trading flat, while Ukraine's hryvnia gave up early gains to trade 0.3% lower.

With sanctions at the ready, the United States and Britain started withdrawing diplomats' family members from Ukraine as talks with Moscow and the West thus far have made no headway.

"A hawkish Fed and Ukraine-Russia risks may very oddly manifest as "risk off" resonance," Mizuho analysts said in a note.

"EMs may feel the heat more acutely as the woes of rising rates and tighter liquidity will be compounded by a stronger USD exposing EMs to higher imported inflation, greater twin deficit slippage and vulnerabilities from external USD-denominated debt."

"In that context, (the) Russia-Ukraine threat... present(s) real challenges in terms of rising oil/energy prices and (a) sharp liquidity/USD squeeze."

Russia's 10-year OFZ bond yields rose to 9.50%, heading back towards their highest since early 2016.

Russia is also grappling with rising COVID-19 cases, which hit a record 63,205 on Sunday.

Ukraine dollar bonds steadied.

Turkey's lira slid up to 2.3% on Monday before recovering to rise 0.4%.

During a weekend conference Finance Minister Nureddin Nebati said no interest rate hikes were planned, but added that he expects some $10 billion of forex bank deposits to be converted to lira due to a new law exempting such deposits from corporate tax.

China's Alibaba slumped 6.3% after a report that its Ant Group affiliate is connected to a corruption scandal involving the former party secretary of Chinese technology hub Hangzhou.

Mainland Chinese shares were largely unscathed thanks to a slew of monetary policy stimulus measures from the central bank last week.

Struggling property developer China Evergrande Group firmed 3.9% after it named a state firm official to its board. The sector will likely see "significant easing" in the policies that govern it, BNP Paribas Asset Management said in a note.

For GRAPHIC on emerging market FX performance in 2021, see http://tmsnrt.rs/2egbfVh For GRAPHIC on MSCI emerging index performance in 2021, see https://tmsnrt.rs/2OusNdX

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(Reporting by Susan Mathew in Bengaluru; Editing by Jan Harvey)