The newspaper said that the source declined to disclose information on when and where the accord would be signed and how many helicopters Pakistan would buy.
According to the Dawn, Pakistan has been pursuing the helicopter purchase agreement since 2009.
The information about the two countries being close to finalizing the deal came shortly after the conclusion of Pakistani Army Chief of Staff Raheel Sharif’s three-day visit to Moscow.
Commenting on General Sharif attending a meeting on the proposed technical accord during the visit, the source said that "there was significant movement towards operationalizing the defense accord, including defense acquisitions."
Apart from helicopters, Pakistan also expressed interest in purchasing other Russian military hardware, according to the newspaper.
Earlier, it was reported that Russia plans to supply the Mi-35 attack helicopters to Pakistan to help it contain drug trafficking.
A version of the Mi-24 Hind attack helicopter produced for export, the Mi-35 utilizes high-precision weaponry for destroying ground-based armored targets and providing air support for ground missions. The helicopter can be modified for use in attacks, medical evacuations or transport.
Meanwhile, the Pakistani delegation has highly praised the International Military-Technical Forum Army-2015 taking place in the Moscow Region, according to Maj. Gen. Asim Saleem Bajwa, the director general of the Inter-Services Public Relations (ISPR), the media wing of the Pakistan Armed Forces.
"The whole expo was overwhelmingly impressive. The airshow, tanks display and firepower demonstrations along with combat hardware demo were out of this world and extremely impressive. We [are] really impressed with the quality of the Russian Armed Forces and Russian military equipment," Bajwa told Sputnik.