The centre-back has been heavily linked with a summer switch to the Emirates after impressing in Ligue 1 during the 2018/19 campaign.
10Sport reports that progress is being made and the Gunners are pushing the hardest to secure the signature of the 18-year-old, who has also attracted the interest of Manchester United.
The transfer could be finalised in the next few weeks, although Saint Etienne have made their requirements clear.
The Ligue 1 side want a fee of around €30 million and the guarantee of having the player return to them on loan for the 2019/20 season.
Saliba made 16 league appearances for his club last season, helping them to a fourth-placed finish in Ligue 1.
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