In a Facebook post, Anwar said he discussed Malaysia's application with Russian Foreign Minister Sergey Lavrov during a courtesy call today.
Russia currently chairs BRICS, which comprises Brazil, Russia, India, China, South Africa, Iran, Egypt, Ethiopia and the United Arab Emirates, The New Straits Times reported.
It is considered the foremost geopolitical rival of the G7 bloc.
"This potential membership holds substantial promise for both nations and underscores our commitment to fostering robust international collaboration," said Anwar.
"We also explored avenues to enhance bilateral cooperation in key areas such as investment and trade, science and technology, agriculture, defense and military, education, and tourism and culture," he added.
Anwar said he also discussed pressing global issues with Lavrov including the ongoing situation in Palestine.
"This engagement reflects our shared dedication to addressing global challenges and advancing a cooperative international agenda."