* Gains in local shares raise hopes for inflows * Dollar's losses against majors helps rupee sentiment (Updates to mid-morning) MUMBAI, Feb 19 (Reuters) - The Indian rupee rose on Thursday as exporters sold dollars on a view a sharp sell-off in the local currency this week was overdone. Opening gains in the share market also offered support. At 10:40 a.m. (0510 GMT), the partially convertible rupee was at 49.88/89 per dollar, off a high of 49.81 and marginally higher than Wednesday's close of 49.92/93. The rupee fell to 50.10 on Wednesday, its lowest since Dec. 3. The rupee had hit an all-time low of 50.65 on Dec. 2. "Asian stocks are a bit in the green (higher), the Dow Jones closed flat, so expecting some recovery in local shares," a senior dealer with a private bank said. "Besides, the recent fall in the rupee was pretty sharp, so there is also some profit-taking and bargain hunting. Exporters are also selling dollars at these levels," he added. At Wednesday's close, the rupee had fallen 2.5 percent against the dollar this week. Indian shares .BSESN rose more than 1 percent in early deals, unwinding some of the 6.4 percent fall of the previous three days, on renewed hopes for an interest rate cut. [.BO]. India's central bank chief said on Wednesday there was room to cut interest rates, but the question was when, whether it should do so and by how much. [ID:nBOM149009]. Fund flows in and out of the stock market have been a key driver for the rupee in recent years. Foreigners have withdrawn about $1.2 billion from Indian shares in 2009, after pulling out more than $13 billion in 2008. The dollar index <=USD>, a gauge of the U.S. unit's performance against majors, was down 0.2 percent, also helping support the rupee. (Reporting by Swati Bhat; Editing by John Mair)

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