There was no immediate official confirmation of the blasts and Reuters was not able to independently verify the reports.
The RBC-Ukraine news agency reported that two explosions took place.
The Russian news outlet Baza reported, citing local residents, that air raid sirens were wailing and an explosion was heard.
Previous attacks against Russian and Russian-occupied targets
The air base, near the city of Saratov, about 730 km (450 miles) southeast of Moscow, was hit on Dec. 5 in what Russia said was Ukrainian drone attacks on two Russian air bases that day.
Two weeks ago, Ukraine launched missiles at targets in the Russian-occupied city of Melitopol in southeastern Ukraine, killing two people and injuring 10 others, Reuters reported, citing reports by pro-Russian authorities.
The report also cited Oleksiy Arestovych, an advisor to Ukrainian President Volodymyr Zelensky, as saying that the city, a major transportation and industrial hub, is critical to the defense of southern Ukraine.
Governor of Russia's Saratov region: information about 'incident' at Engels military base being checked
Russia's governor of Saratov region, home to the Engels air-base, said early on Monday that law enforcement agencies are checking information about "an incident at a military facility."
"There were no emergencies in residential areas of the (Engels) city," Roman Busargin, the governor of the region, said on the Telegram messaging app.
"Civil infrastructure facilities were not damaged."