Hodgson is facing up to a defensive crisis as he prepares for the World Cup qualifying double header against San Marino and Poland after John Terry quit the international scene, while Glen Johnson is suspended.
And Arnesen believes former Chelsea defender Mancienne is the ideal candidate to fill the holes left by Terry and Johnson following a string of impressive displays for the Bundesliga side.
"If I was the coach then I would definitely look at him, absolutely," Arnesen told the Daily Mirror. "He could be a good shout for the squad as he can play right-back and centre-back. He has been outstanding.
"We won against Hannover on Saturday and it was the best performance he’s played in his 16 months since he came here.
"I think the Bundesliga is as tough as, or tougher than, the Premier League because the rhythm of the league is very high and it’s physically tough.
"He has learnt so much from coming here. Not many English players go abroad but he's improved through doing it. He's developed as a player and as a person.
"He is not the tallest and yet his leap is unbelievable. He can jump so high. He is a aggressive in a good way, he is quick and good on the ball.
"When you play for England, it's a different style of football. You're playing international opponents and it helps if you've experienced playing regularly against different opponents with a different style and Michael has done that here."