Mane believes the 29-year-old Napoli defender would be a huge hit for the newly-crowned Premier League champions.
The duo were clubmates at Metz in 2011-12, and have played together many times for Senegal's Teranga Lions.
Mane, 28, said: "Kalidou Koulibaly is an excellent defender, and one of the world's best in his position.
"I would be very happy to play alongside him at club level, as I have known him for years."
The winger continued: "We first got to know one another at Metz before meeting up once more in the Senegal national team.
"No club could refuse the chance to have Koulibaly in their squad.
"In any event, it would be a pleasure for me to play for Liverpool together with him.
"He would be more than welcome here."