Airport is set to be handed over early next year — almost two years behind its programmed completion date of April 2014.
The new terminal is currently being built as part of a $1.8bn upgrade of Muscat International Airport, which also includes new runways and infrastructure.
The terminal building is being carried out by a consortium led by US contractor Bechtel, alongside Turkey's Enka and local firm Bahwan Engineering.
In an interview with Construction Week, Bechtel's Europe, Middle East and Africa president David Welch, said: "We are very far along with that project."
"This is a complex, large airport project so it has quite a number of other moving pieces. We have made, particularly recently, very good progress with the building."
"It's going up very fast now because all of the structural steel is almost all in place, the cladding is going on so the MEP systems are going inside, the stonework is going up... When you drive by it now you will see something that looks much more like an airport."
Welch added that Oman's Minister of Transportation, Dr Ahmed bin Mohammed bin Salim Al Futaisi, has been a frequent visitor to the site and is "very attentive" to the project.
"Obviously, it's a centrepiece for the Sultanate. He has made a number of statements about his expectations and he has targeted an opening for full operation of 2016. So here we are at not quite the beginning of 2015 and we're full pedal to the metal in getting that to where he would like it to be by the beginning of next year so he can operate it during the year."
Bechtel's consortium was awarded a contract to build the airport in 2011. It has faced a number of challenges along the way, including the sinking of a shipment of steel that was destined for the project in April 2013 and a strike by workers over safety conditions.