Christensen is in the final six months of his contract at Chelsea and currently appears almost certain to leave Stamford Bridge at the end of the season.
Negotiations over a new deal between Chelsea and his agent have stalled and for the moment there are no conversations between the two sides.
His agent has been talking with clubs across Europe with a view to finding a new club for the Dane in the summer.
And according to German magazine Sport Bild, Dortmund are amongst the clubs who are keen to get their hands on Christensen at the end of the season.
The 25-year-old defender is rated highly in Germany where he spent two good years on loan at Borussia Monchengladbach.
Dortmund are looking to reinforce their defence next season and Christensen is one of the players the club are keeping an eye on.
Barcelona have also set their sights on the Dane and are keen to get their hands on him on a free transfer as well.
It remains to be seen if Chelsea look to revive the talks for a new deal with the defender in the coming months.