The BRICS group also includes the major emerging economies of Brazil, India and South Africa.
“The BRICS interest us” as an alternative to traditional power centers, Tebboune said in a televised interview late Sunday. “They constitute an economic and political force.”
He underlined that there was no need to “get ahead of things” but promised “good news”.
The president added that his North African country meets “a good part” of the economic criteria for joining the bloc.
BRICS members currently account for nearly a quarter of the world’s gross domestic product.
Tebboune participated in a BRICS virtual summit at the end of June, when Putin called on leaders of the group to cooperate in the face of “selfish actions” from the West.
Sanctions over Ukraine have pushed Putin to seek new markets and strengthen ties with countries in Africa and Asia.
Algiers abstained when the United Nations General Assembly overwhelmingly passed a resolution in March demanding Russia immediately withdraw from Ukraine.
China, India and South Africa also abstained.
On a visit to Algeria in May, Russian Foreign Minister Sergei Lavrov said trade between his country and Algeria had reached $3 billion last year.