Arsenal made the 18-year-old a key transfer target this summer and have now reached an agreement with the Ligue 1 side.
Saliba joined Saint Etienne’s youth set-up in 2016 and signed his first professional deal at the age of 17 last year.
The 6’4″ central defender has made 16 league appearances for the club since making his debut last season and represents the France Under-20 side at international level.
Saliba is known for his aerial threat and tackling ability, and could serve as a long-term replacement for his fellow Frenchman Laurent Koscielny.
Sky Sports have reported that Arsenal and Saint Etienne have agreed a ‘deal in principle’ which comes after Tottenham held talks for the player.
The rumoured fee is currently undisclosed, but The Sun have reported that the price will be £27million plus add-ons.
The deal is likely to involve the defender going back to his former club on a season-long loan, which means Arsenal still need to solve the problem surrounding their club captain.
The Gunners revealed their disappointment last week when Koscielny refused to travel with his team-mates to begin their pre-season tour.
Sky sources also claim that Arsenal are willing to let the veteran leave – but only if their valuation of the 33-year-old is met.
Another likely incoming deal at the Emirates is one for promising Brazil international Everton Soares.
Spanish outlet Marca have claimed that the club are nearing a £36m deal for the Copa America top scorer, which could see Wilfried Zaha miss out on his dream move.
The report claims that Everton, 23, will join the club as an alternative to Zaha rather than a possible team-mate, with Crystal Palace requesting £80m for their star forward.
Unai Emery has promised fans that the club are currently pursing several deals to improve their playing squad, which could refer to both Saliba and Everton.
“Our target is to achieve three, four players to really improve our team and squad now,” he said.
“We are being very demanding and we are also first speaking about the possibility to sign very big players, very expensive.
“We are having a lot of meetings with the club, with [technical director] Edu, also with Josh and Stan Kroenke in Denver. We have a very clear idea: to sign the players who can help us with a good performance and in the positions we need.”