The 25-year-old Danish international is currently in the middle of a season-long loan spell with Serie 'A' giants Juventus, but has only started three games for Antonio Conte's side this campaign.
Arnesen feels that the Gunners star's ambition might be holding him back a little, and having failed to make the grade at the Emirates Stadium, should consider dropping down to a lesser side in order to gain regular first-team action.
"He must take a step down and choose a good club where he can rediscover the joy of playing and play a lot," said the Hamburg chief. "He said no to me twice because he wanted to play in an even bigger club.
"He must make sure he is always in the best shape and so he should be more humble and think about how he can get the most out of his talent."
Arsene Wenger looks to have finally given up on a player that was earlier this month banned from representing his country for six months, after being arrested for drink driving.
Bentner, who has scored 22 goals in 55 international appearances, was handed the punishment by the Danish Football Association, and in doing so, has probably put the final nail in his Arsenal coffin.
Speaking to Russian daily, Izvestia, Bendtner's agent, Tom Brooks, said that his client has received offers to move to Russia, when his contract in Turin finishes at the end of the season.
"We've had contact several times with Russian teams. In addition, interest has been shown in Nicklas by English and Italian clubs and the player would like to play regularly in the Champions League.
"In recent years a large number of talented players have gone to Russia. And if a solid proposal arrives, we will consider it before deciding Nicklas's future."