The French outlet claim that Manchester United and Manchester City are also keen on the player.
But it is Arsenal that they say offer a "framework conducive to the progression" of the 18-year-old who played 16 matches in Ligue 1 last season.
It's believed that Saint-Etienne need to raise funds to make squad improvements of their own, but ideally they would like to keep Saliba on loan for another season.
Whether such a temporary solution is included in Arsenal's proposal is unclear, but the Gunners are operating on a limited budget – not least after their failure to qualify for the Champions League.
Previous reports indicate that Saliba could cost around £25 million.
He is currently with France at the Under-20 World Cup in Poland.
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