Arsenal boss Unai Emery is keen to strengthen his side this summer, though is believed to be on a tight financial budget.
It’s believed Emery has £40million to spend this summer after a January window where he could only bring in loan deals.
Emery sees defence as a priority and Saliba has shone at centre-back for Saint-Etienne in Ligue 1.
French outlet Le 10 Sport claim Arsenal are in advanced talks with the 18-year-old.
But it’s believed Saint-Etienne have put a €30million (£26m) price tag on the defender.
That would take up over half of Emery’s budget and leave the boss struggling when it comes to strengthening other areas.
Saint-Etienne are also believed to only be keen on sorting a deal if they can keep their defender on loan for next season.
Former Arsenal star Lauren has praised the teenager.
“Yes, he looks a very good player,” Lauren said.
“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!”
Saliba’s agent was spotted in the UK earlier this week.
That sent Manchester United fans into frenzy with agent Djibril Niang uploading an Instagram story from Manchester.
Saliba made 16 appearances for the Ligue 1 side in his break-through season, in which Saint-Etienne finished fourth.
The defender has also earned the praise by former Chelsea and Manchester United boss Jose Mourinho.
“I think he has everything needed to become a good player, much like Kurt Zouma, who I signed,” Mourinho said.