By Russian law, foreigners found guilty of spying on Russia face between 10 and 20 years in jail.
A member of the US government should have visited Whelan in detention by now, according to Russia's obligations under the Vienna Convention, which dictates that consular access must be provided within a 72-hour window from the time of arrest.
But the US government shutdown may have hindered this process, said a person familiar with Whelan's case.
Although US embassies are not closed during the shutdown, they are working with reduced staff. The person added that it could take months before the case is resolved.
Whelan's arrest comes as tensions between Washington and Moscow continue to escalate over issues including election interference, the crises in Syria and Ukraine, and the poisoning of a former Russian spy in Britain.
Whelan works as the corporate security director for BorgWarner, an automotive parts supplier based in Auburn Hills, Michigan, that has business contracts in Russia.
"BorgWarner has reached out to the US government to do their best to learn about this situation, and bring Paul home," the person familiar with the case said.
Whelan is a regular visitor to Russia. According to Whelan's brother and Russian acquaintances, he has been visiting Russia since 2007, when he was a Marine staff sergeant serving in Iraq and travelled to Moscow during a break from duty.
Several Russian acquaintances described Whelan as a friendly man who greatly appreciated Russia and had a basic command of the language.
An acquaintance in St Petersburg said the pair had made plans to meet in that city around January 1, but contact with the American abruptly stopped on the day of his arrest.
The timing of Whelan's arrest - coming weeks after Russian gun rights activist Maria Butina pleaded guilty to Kremlin interference in the United States - has raised questions about a potential swap. The two countries do not have an extradition treaty.
The arrest and guilty plea by Butina, 30, has become a sharp thorn in the side of US-Russian relations.
Butina is the first Russian national to be convicted of seeking to influence US policy in the 2016 election campaign. Moscow has gone to great lengths to paint her as a political prisoner.