The Bundesliga outfit – who scored fewer goals than any other side in the top half of the table last term – are keen to bolster their attacking stocks with the 27-year-old.
Jelavic arrived at Goodison Park from Rangers in January 2012 and was an immediate hit, scoring 11 goals in 16 appearances to finish the 2011-12 season.
He was not as prolific last term however, scoring just eight times in 43 games, and the close-season arrivals of Barcelona loanee Gerard Deulofeu and Ivorian Arouna Kone have put Jelavic's Everton future in doubt.
Hamburg are keen to seize the opportunity and sporting director Oliver Kreuzer has been a keen admirer of the striker for some time.
Kreuzer told Hamburger Morgenpost: "He is a player of class.
"I know Nikica very well. I tried to transfer him from Rapid Wien to Sturm Graz (where he formerly worked as sporting director) in 2012 before he moved to Glasgow Rangers. We almost sealed a deal.
"He was offered to us (by Everton) and isn't wanted there any longer. We (are) working on it right now. He has an edge, he is able to play nasty."
Kreuzer revealed that Hamburg will have to bring in some money though, before they step up their attempts to secure the forward.
"Unfortunately we are not that far (along with talks). To finance him we need to sell two to three players. And there is nothing official yet.
"Who knows whether Nikica will like to stay at Everton or has a new club in two weeks' time."comments