French outlet Foot Mercato claim Arsenal are in talks with Tours over a six-month loan deal.
The report does not mention whether the deal includes an option to buy at the end of the six months.
Bennacer joined the Gunners from Ligue 2 side AC Arles-Avignon in 2015.
Arsenal midfielder Ismael Bennacer is closing in on a move to Tours
But the Algerian has so far made just one first-team appearances for the club.
That came in the 3-0 League Cup defeat to Sheffield Wednesday last season.
Despite his lack of game time at Arsenal, the midfielder is already an Algeria international.
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Ismael Bennacer has made only one first-team appearance for Arsenal
The 19-year-old, who played at under 18 and under 19 level for France, made his international debut for Algeria back in September after switching allegiance.
And he was recently a late call-up for the Algeria squad for the Africa Cup of Nations as a replacement for the injured Saphir Taider.
But the youngster didn’t play a single minute as Algeria went crashing out of the competition after failing to win any of their three Group B matches.