Norway's wealth fund is making final preparations for its first Asian real estate investment as it builds a portfolio of properties in the world's biggest cities.

After scouring Asia for investment opportunities, the $870 billion fund, built from Norway's oil revenue, has narrowed its search to Singapore and Tokyo, said Karsten Kallevig, head of real estate investments at the Oslo-based fund.

"Tokyo is arguably the single biggest market in the world for real estate," he said in an interview Friday. While the fund doesn't have an ultimate spending target, "we can invest a lot in Asia," he said.