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The 42-year-old Swede - who was a member of the Arsenal "Invincibles" side under Arsene Wenger in the 2003/04 season 3 has been put in charge after Unai Emery´s undistinguished 18 month reign came to an end on Friday.
Arsenal legend and Nice coach Vieira has also been mentioned as an option and Dixon believes the former club captain would be the ideal appointment for the Gunners.
And Carragher said he too was baffled by Ljungberg's picks, highlighting the inclusion of Mustafi as particularly puzzling.
Ljungberg took training for the first time at 11am yesterday and there is a sense that he could persuade club chiefs to follow Manchester United's example from last season if he makes a big impact in the role.
The current team are winless in seven games, their worst run in 27 years.
Arsenal are now 8th on the Premier League table, and a top 4 finish is starting to look increasingly unlikely with every point dropped.
Ex-Sweden global Ljungberg, 42, played for Arsenal from 1998-2007, winning two Premier League titles and three FA Cups with them. "They just said concentrate on your next game do as well as you can", he said.
"No, no indication of how long or how short".
"It is a great, great honour, that is how I feel".
Whoever occupies the vacancy should not expect that the club's ambitions for the season will be more contiguous due to their hard start, as Kroenke - the son of Stan club owner - still feels they can achieve their goals. I feel this energy inside of me. The former Arsenal midfielder reacted to the speculation after Nice's win over Angers on Saturday evening: "It's a very hard job and I realise that". If you play good football and have a good result, there's nothing better to raise spirits.