Putin, who visits India on Monday, has his sights set on selling 42 Sukhoi SU-30MKI fighters and on the long-term supply of 970 warplane engines, one of the sources said.
The source did not put a value on the deals because, he said, the size of the orders had not yet been agreed.
"There is no total figure for the volume of engine contracts. It depends on what they (India) order," he said.
But another industry insider said the contracts could bring in at least $7.5 billion for Russia, one of the world's largest arms exporters.
"The deals are expected to be announced during Putin's trip to India," said Ruslan Pukhov, director of the Russian defence think-tank CAST. "The price for everything together will be between $7.5 billion and $8 billion."
The Russian Defence Ministry and the Kremlin declined comment.
If concluded, the deals would boost a Russian industry whose export market has shrunk since last year's Arab uprisings.
India, cautiously watching regional rival China's growing military might, has been the top importer of Russian weapons.
The Russian arms industry, nurtured under Putin's first presidency from 2000 to 2008, has sold weapons to post-Soviet states and Cold War allies for decades on the strength of Soviet-era technology.
But the industry has largely stagnated due to a lack of funding since the collapse of the Soviet Union, leaving weapons manufacturers dependent on outdated designs.