The possibility of talks emerged after the summit in Finland between US President Donald Trump and Russian President Vladimir Putin.
"Two US officials, speaking to Reuters on condition of anonymity, said Mattis was open to the possibility of talks. They did not suggest he was actively seeking discussions with Shoigu, either in person or by telephone."
Last week, Shoigu said in an interview with Italy's Il Giornale newspaper that he firmly believed that all the disputes should be settled peacefully and without the use of military force.
"There is only one communication channel between our general staffs now, which is used in negotiations, including at the level of the chiefs of general staff, aimed, first of all, at preventing the military activities of Russia and the United States from turning into a military conflict between our nuclear powers," Shoigu said.
The last talks between the US and Russian defense ministers took place in 2015, when Shoigu spoke with then-US Secretary of Defense Ashton Carter. The two senior military officials then agreed during a phone conversation to resume Russia-US military contact, and to continue discussions to ensure a peaceful resolution to the Syrian crisis.