Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Knoxville to Reykjavik as you normally would.
August can be a great time to fly to Reykjavik from Knoxville with a flight ticket averaging about $935. Cheapflights users have found deals in the month of August for as cheap as $586. The most expensive prices can be found in the month of November.