The Gunners have been monitoring the 18-year-old’s situation following a strong campaign for the Ligue 1 outfit.
Saint Etienne want £26m for Saliba this summer.
And Le10 Sport are reporting that Arsenal are willing to pay that fee – but may be forced into loaning the youngster back to France for another season.
The French publication claims both parties are still locked in negotiations.
However, a deal is still close enough that it could be finalised in the next few weeks.
Manchester United boss Ole Gunnar Solskjaer is looking to add quality to a backline that struggled last season.
The Daily Record last week claimed the Red Devils have turned their attentions to Saliba after reports revealed the defender’s agent was spotted in the city.
Djibril Niang was seen dining in Manchester city centre restaurant Ivy Asia yesterday.
Watford and Southampton also reportedly interested in the the France Under-19 international.
Ex-Arsenal star Lauren is convinced by Saliba’s potential after watching the teenager’s recent performances in France.
“Yes, he looks a very good player,” Lauren told AmericanGambler.com.
“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!”
The Gunners, meanwhile, appear to be also focusing their efforts on signing Jordan Veretout.
L’Equipe reported they have made an official move for the Fiorentina midfielder.
Arsenal are also said to be in talks with Dalian Yifang star Yannick Carrasco.
The Belgian was heavily linked with a move to the Emirates in January.
Carrasco has repeatedly stated he is ready to leave China after only 16 months in the country.