The French side have enjoyed a brilliant first half of the season and currently sit top of Ligue 1 after 19 games.
Nice are now looking to add to their squad during the January transfer window as they try to continue their title push.
And, according to L'Equipe, Porto winger Brahimi is right at the top of manager Lucien Favre's shopping list.
Brahimi, 26, has impressed this season and has so far bagged four goals in 12 games in Portugal.
Nice's interest will come as a blow to Everton, though, who are also interested in the Algerian after failing with an approach in the summer.