"We are in a dilemma," Danthine told the Basler Zeitung daily in an interview.
"For the real estate sector, interest rates are clearly too low at the moment," he said, adding that low rates created "fertile ground for excesses."
Danthine said he hoped the European Central Bank would raise rates soon, which would give the SNB "more room for manoeuvre".
The International Monetary Fund (IMF) said in its assessment of the Swiss economy this week that the central bank should be in a position to tighten borrowing costs in the near-term, barring any more shocks.
The IMF also called for the authorities to keep a close eye on the booming Swiss housing market, warning of lax lending standards in the mortgage market.
SNB vice-chairman Thomas Jordan said in an interview this week the franc's surge against the dollar limits the central bank's leeway to raise rates.
At its quarterly monetary policy meeting earlier this month, the SNB kept interest rates ultra-low despite an overall improved outlook for the economy, citing risks from Europe's debt crisis and the Japan disaster.
But the central bank dropped any reference to deflation risks in its statement and raised its growth forecast, which economists said opened the door for rate hikes later this year although the record-high franc remains an obstacle.