The 18-year-old has been heavily linked with a move to Arsenal in recent times but there has also been interest from Manchester United and Manchester City.
According to Foot Mercato though, the Gunners have won the race for the Frenchman and have agreed a five-year deal with him.
All Arsenal need to do now is agree a fee with Ligue 1 side Saint-Etienne, but this could prove to be a stumbling block.
The French side are believed to want around £26m for Saliba but this would take up over half of Unai Emery’s summer transfer budget.
The club’s failure to secure Champions League football next season means there will only be around £40m to spend, it is believed.
Saliba has been identified by Arsenal as a potential replacement for Laurent Koscielny, with the 33-year-old a reported target for Borussia Dortmund.
Saint-Etienne are willing to sell him if they can have the French youth international on loan for next season, but the Gunners are understood to not be keen on the proposal.
Borussia Monchengladbach and clubs from Serie A are also thought to be interested in the defender, as well as the Premier League clubs.
Saliba’s agent recently fuelled speculation that his client was set for a move to a Manchester side after sharing a picture of himself in the city.
It was a breakthrough season for the talented youngster last campaign, as he featured in 19 games in all competitions.
The highly-rated teenager only extended his contract at Saint-Etienne in April after impressing for the first team over the last season.
A club statement read: “This Tuesday, William Saliba has extended his two-season contract with his training club which he is now bound until 2023.
“A pledge of confidence placed on the qualities of the young man of 18 years whose benefits reflect an irreproachable state of mind.
“His extension of contract also proves the ambition of the club.”
Meanwhile, David Ospina is leaving Arsenal after Napoli took up their option to buy the goalkeeper.
Colombian international Ospina impressed boss Carlo Ancelotti on loan at the Serie A side last term.
And the club have retained the Colombian’s services after paying £3.5m to keep him at the San Paolo.