After a slow start to life at City after joining the club in January 2011, Dzeko hit form at the start of this season, scoring ten goals in the club's first eleven league matches.
However, he has yet to hit the back of the net since scoring in a 3-2 win over QPR on November 5, and has been dropped in favour of Sergio Aguero and Mario Balotelli, who have both impressed when handed their chances.
While it remains unlikely that the Bosnian international will be leaving the club any time soon, Elber feels a move to Bayern would benefit both player and club, especially considering Dzeko's successful spell in Germany with Wolfsburg.
"He [Dzeko] is definitely a candidate, in my opinion," Elber told TZ. "He has already proven his worth in the Bundesliga.
"And if you have the chance between warming the bench at Manchester City or joining Bayern Munich, moving to Bayern is the preferred option, right?"
Aware that his suggestion is unlikely to happen in the future, Elber then went on to suggest another striker who could be a more realistic option for the Bavarian outfit should they decide to bolster their options - Werder Bremen's Claudio Pizarro.
"Claudio would fit in very well at Bayern," Elber added.
"He has a lot of quality and is at an age where he doesn't necessarily needs to play every game."
Pizarro played for Bayern from 2001 to 2007, and scored 100 in 251 appearances before leaving for Chelsea ahead of the 2007/08 season.