A fresh stimulus by the Fed would spur dollar inflows into emerging markets and is likely to boost risk currencies like the rupee.
The euro eased but stayed close to a near four-month peak hit on Friday after below-forecast NFP data, with sentiment being largely positive after the European Central Bank unveiled its plan to cut borrowing costs for the indebted peripheral countries.
"Despite the euro's overnight strength, the dollar was well bid in the domestic market by oil companies," said Hari Chandramgathan, a forex dealer with Federal Bank.
Oil is India's biggest import, with refiners the largest buyers of dollars in the local currency market.
"The pair should trade in a range of 54.85 to 55.85 for the week with inflation data on Friday and the movement in the euro and other majors being key for direction," Chandramgathan added.
The partially convertible rupee closed at 55.44/45 per dollar, versus its close of 55.3550/3650 on Friday.
Traders said they would monitor the factory output data on Wednesday, ahead of the August inflation data on Friday, and also the more volatile of the two, for cues on central bank action at its policy review on September 17.
The index of industrial production is seen to edge up 0.3 percent year on year in July, according to a median forecast of 30 economists, after shrinking 1.8 percent in June, which was the third contraction in four months.
The one-month offshore non-deliverable forward contracts closed at 55.71, while the three-month closed at 56.34.
In the currency futures market, the most-traded near-month USD/INR contracts on the National Stock Exchange, the MCX-SX and the United Stock Exchange, all closed at around 55.54 with a total traded volume of around $2.79 billion.