The 18-year-old enjoyed a breakthrough season at the Ligue 1 side, making 19 appearances in all competitions.
The 6’ 4’’ defender helped Saint-Etienne achieve a fourth-place finish in Ligue 1 and has reportedly attracted interest from around Europe due to his impressive displays last season.
Arsenal and Manchester United are said to be keeping track of the teenager and are open to the idea of a move this summer.
Initial reports suggested United were frontrunners to sign Saliba after his agent was spotted in Manchester, but it now seems Arsenal are most likely to acquire him, according to Le 10 Sport.
The French publication claim the Gunners are now in advanced talks to sign Saliba and could have the deal done in the coming weeks.
Its thought that Saint-Etienne are looking for £25million for the young centre-back, and Watford and Southampton are also interested in his services.
Arsenal legend Lauren has praised Saliba and believes he has the potential to succeed having watched him perform last season.
Lauren told AmericanGambler.com:
‘Yes, he looks a very good player
‘Strong, tall, can come out of the back with the ball and an international for France.
‘He reads the game very well, which is important for a player at the back, you have to anticipate and he looks very good at just 18, so the future is bright!’
Arsenal defensive frailties were once again evident last season and it’s believed Unai Emery will address the situation during the summer transfer window.