The pair had settled at 58.79/80 on Friday, after the rupee earlier hit its highest level in 11 months at 58.62 per dollar.
Gains in most Asian currencies against the dollar may add to further weakness in the pair.
Foreign investment flows into shares and debt will be key for the rupee, while dollar buying from the central bank is also expected to cap broader gains in the rupee.
The pair was trading at 58.54/56 in the spot NDF market in Singapore.
NSE index futures traded on the Singapore Exchange rise 0.88 percent, while the MSCI-Asia Pacific excluding Japan index falls 0.24 percent.
The index of the dollar against six major currencies down 0.05 percent.
The pair is seen moving in a 58.50 to 59.00 range during the session.