The Premier League heavyweights failed to catch the 17-year-old striker last week.
But according to Sun, they are still desperate to secure their signature even though the transfer window is closing.
However, it is suggested that Unai Emery could lose the hit man.
Red Bull Salzburg is willing to pay 7 million pounds sterling for his signature and will have until the end of the month to do so.
"The head of the Arsenal, Unai Emery, is interested in Erling Haaland"
The Gunners see Haaland, who is the son of former Manchester City ace Alf-Inge, as a hot prospect and will not give up the pursuit if Salzburg catches him.
They are ready to plummet in 12 months, even if this means taking them away from the Austrian team.
Emery's team fought in their presentation of the Premier League this afternoon.
They lost 2-0 to Manchester City, who were comfortable throughout the game.
Speaking after the confrontation, Emery claimed that his side is a work in progress.
He said: "The result was 2-0, but I think that on the pitch in the 90 minutes we were improving.
"The first half did not play as we wanted.
"We talked at halftime about taking more responsibility for the second half, to do a little more.
"We wanted to build with the ball and break their lines.
"I think in the second half we play more as we want."
Matteo Guendouzi, who was signed from Lorient in the summer, impressed during the clash.
Emery quickly praised the 19-year-old midfielder.
He added: "It's their first match here in the Premier League.
"He has personality and quality, and if he's on the pitch, he's improving very fast.
Emery signed five players during this transfer window while reorganizing his squad.
Stephan Lichtsteiner, Sokratis Papastathopoulos, Lucas Torreira, Bernd Leno and Guendouzi were selected.
Arsenal has a trip to London to face Chelsea at Stamford Bridge next to the schedule.
The Blues gave way to a 3-0 victory over Huddersfield in their opening.