The Swede took charge of his last match in a dire 0-0 draw with Everton - making it one win in six for the part-time manager.
Gunners chiefs have sounded him out about joining Arteta's backroom team but the 42-year-old, who has been linked with Malmo, wants to meet the Spaniard first.
He told BT Sport: "I've been told by the club they want me to stay but I will have a meeting with Mikel tomorrow and hopefully it's a good one."
On the game, Ljungberg added: "I thought we could have won the game with the chances we had. But I loved the spirit we saw and that's what you need in the Premier League.
"I wanted to see people that would run and fight for the team. We can't rely on our name - we have to fight and do the dirty things."