Saliba has attracted interest from a host of clubs this summer after cementing his place in Ligue 1 last season.
Arsenal, who have made a centre-back one of their top priorities in this window, have reportedly been working on signing the 18-year-old since April.
According to Telefoot (TF1), Arsenal faced late competition from bitter rivals Tottenham.
However, Telefoot understand that Saint-Etienne will sell Saliba to Arsenal and the Gunners are now believed to be finalising a deal worth €30m.
There are said to be some details to settle in a move that would see Saliba loaned back to Saint-Etienne for the 2019/20 campaign.
Saliba featured for France Under-21s at this summer's European Championship.
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