HSV sporting director Frank Arnesen held talks with Stevens over the weekend but returned dissatisfied after the Dutchman indicated he also wanted to meet with Schalke.
Both Hamburg and Schalke are searching for a new coach after the former sacked Michael Oenning last week while Ralf Rangnick resigned from the latter due to exhaustion.
Schalke now appear to be favourites to snare 57-year-old Stevens, who enjoyed a successful 16-month spell at Hamburg between 2007 and 2008.
After Arnesen was reported to have claimed HSV wanted a coach who was "100% committed to them", Stevens said: "That surprises me.
"Schalke are also in the race. I've been honest with Frank Arnesen and I have listened to everything."
Rodolfo Cardoso was in interim charge as Hamburg won their first game of the season, at Stuttgart on Friday night, while Seppo Eichkorn, Rangnick's temporary replacement, was also victorious as his Schalke side beat Freiburg 4-2.
Hamburg meet Schalke next Sunday at the Nordbank Arena.