* USD/INR seen opening at around 61.95 versus its close of 61.74/75 on Friday, helped by demand for the greenback from importers. * The dollar's index against six major currencies currently up 0.03 percent. * Most other Asian currencies however trading stronger compared to the dollar and could limit sharp gains. * The euro clung to modest gains early in Asia on Tuesday, having bounced off a seven-week low on the back of improving euro zone data, but talk of a rate cut this week should curb demand for the common currency. * The MSCI index of Asian shares ex-Japan trading down 0.14 percent while the Nifty stock futures traded in Singapore down 0.1 percent. Traders will watch domestic shares for cues on foreign fund flows. * Also on watch, India HSBC Service PMI at 0500 GMT. * USD/INR seen trading at 62.04/62.07 in the offshore NDF market.