The Gunners are not thinking about sacking coach Unai Emery imminently.
But the Spaniard is on thin ice, as fans are unhappy with the team's performances so far this season.
If Arsenal do not finish in the top four or win the Europa League, Emery would likely depart.
And notoriously reliable journalist David Ornstein, who works for The Athletic, claims the club see Ljungberg as the natural successor to Emery.
He said: "Freddie is highly-rated by the players and staff, and the logical feeling is he would take temporary charge if anything happened with Emery.
"He has 'number one' ambitions of his own and won't hang around somewhere for too long if he doesn't think the opportunity will come."