The force said the current use of a helicopter is appropriate for quick deployment in urban areas while a fixed wing craft may be suitable for covering remote regions.
At a meeting of the Scottish Police Authority in Glenrothes, Fife, members were asked to approve plans to extend a contract with Bond Air Services for up to two years as they consider the option.
Bond provides Police Scotland with a helicopter at a cost of around £2.4 million a year. Negotiations to extend the contract require Scottish Government approval.
Buying a new helicopter with a 15 to 25-year life span would cost around £6.3 million compared with around £2 million for a fixed wing aircraft which would last approximately 30 years, according to the force.
A report before the meeting said: "Fixed wing aircraft have lower flying charges and a longer flight range which would appear to be suited for policing purposes in more remote areas.
"However, there are more restrictions in the take-off and landing processes."