Sri Lanka opened its first expressway to Galle in the south late last year.
Officials say hotel occupancy is already up in the region after travel time was cut.
Sri Lanka has signed up with Qatar Holdings, the emirate's sovereign wealth fund and its wholly owned unit Qatar Diar Real Estate Investment Company following visit by Qatari ruler, Sheikh Hamad Bin Khalifa Al Thani earlier in January.
Qatar has proposed a large tourism development complex involving seven islets off the coast of Kalpitiya.
"There has to be a feasibility study to find the viability of the expressway," minister Rajapaksa said.
"They say is tourists are not always willing to travel in small planes.
"An expressway will take tourists from the airport in 20 to 30 minutes. So they said if we invest in the islands, we will also invest in the toll road.
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Qatar had also looked at land in Colombo, including land in the Galle Face beachfront, minister Rajapaksa said.
Two blocks in the area has also bee