The report comes amid rising concern among US officials of increased Russian military activity in Syria.
President Barack Obama cast the buildup as an effort to prop up the country's embattled leader, warning Moscow against doubling down on Assad.
Russia, a longtime backer of Syria's government, denies it's trying to bolster Assad and says its increased military activity is part of the international effort to defeat the Islamic State group which has wreaked havoc in Syria and Iraq.
A former Lebanese general with knowledge of the Syrian military told The Associated Press last week that there are plans to build a military base in the coastal town of Jableh, about 25 kilometres south of Latakia city, where the airport currently under development is located. Israeli officials also say the aim appears to be a military base.
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The airport, known by its old name Hemeimeem, already houses a military base and has come under shelling from advancing militants in the countryside.
The head of the Britain-based Syrian Observatory for Human Rights, Rami Abdurrahman, said witnesses, including officials inside the airport, reported that the tarmac was being expanded, apparently to allow for larger planes.
"It could mean there will be more supplies or that they want to turn it into an international airport," Abdurrahman said.
The Observatory relies on a network of activists on the ground to report on the Syrian civil war, now in its fifth year.
More than 250,000 people have been killed and nearly half of Syria's pre-war population of 23 million has been displaced from their homes. About 4 million of them are refugees in neighboring countries.