The Reds boss is ready to bolster his defensive options after strengthening the Liverpool midfield with the captures of Charlie Adam, Stewart Downing and Jordan Henderson.
Reports suggest Dalglish is keen to move for the German international, who endured a difficult campaign with Hamburg last season.
The 25-year-old only managed 17 appearances for the Bundesliga side, with injury problems contributing to his lack of action, as he then struggled to get back into the side following his recovery.
However, Jansen was linked with Wolfsburg earlier in the summer transfer window and stressed his commitment to Hamburg at the time, and it remains to be seen whether or not his stance will change following reported interest from Liverpool.
Liverpool last week