The two parties are considering several options, including an outright sale, Reuters reported citing undisclosed sources.
This JV would be similar to the one formed by the two firms in May 2021 to run their operations in Angola.
The move to sell assets comes as the British firm seeks to refocus its businesses by paring debt while addressing declining margins and climate pressures.
In Algeria, international firms earn fixed royalties for their oil and gas assets, based on production sharing agreements (PSAs), making them less profitable and difficult to sell.
In 2020, BP reported net production share of 141 million cubic feet (mcf) of gas per day and 6,000 barrels of oil per day in Algeria.
The two firms have also pledged to shift away from oil and gas and transition to low-carbon businesses in the coming decades.
This is in line with other top energy companies in Europe considering the divestiture of their oil and gas assets due to increasing uncertainty over demand for fossil fuel in the future.
However, these firms are retaining more profitable assets.