The Gunners are in desperate need of reinforcements this summer following their disappointing first campaign under Unai Emery.
Arsenal have a limited budget to work with in the coming weeks following their failure to qualify for the Champions League.
This means Emery must pick and choose his most sought-after transfer targets.
And it appears Bennacer isn’t the type of player the Spaniard wants to spend his money on this summer.
The Guardian claim the midfielder, who has helped Algeria reach the final of the African Cup of Nations, was offered the chance of an Arsenal return.
Bennacer, 21, made one first team appearance for the Gunners after signing for the north London outfit in 2015.
Two years later he was shipped off the Empoli where he has impressed in recent months, despite the club’s relegation from Serie A.
AC Milan have agreed a deal with the fellow Italian side, paying €16m (£14.4m) plus add-ons for Bennacer.
But a clause Arsenal inserted into the player’s contract when he joined Empoli saw them have first refusal this summer.
Bennacer should now complete his move across Italy in the coming days.
Arsenal are focusing on their defence at present, chasing Celtic full-back and Saint-Etienne youngster William Saliba.
Emery’s side are yet to agree deals for either player.
And Celtic boss Neil Lennon today hinted that the Scottish side were ready to demand more for Tierney in the coming weeks.
“I don’t know what Arsenal’s financial state is, I know what ours is and we are quite comfortable with the situation at the moment,” he said.
“There has been a second bid, the bid has been rejected, and it’s as you were.
“Whether they come in again or not, I can’t answer that.
“He’s a great player and a great talent and at 22 he has already achieved a hell of a lot in his career and has so much more to give to the game.
“It doesn’t surprise me there are potential suitors out there for a player of his quality but he’s our player, he’s on a long-term contract and – while it’s a back-handed compliment for all the work people have done here over the years with Kieran – we don’t want him to go.”