The Germany international is currently training with the BVB as the club considers its defensive options following Neven Subotic's injury
Friedrich is currently training with Dortmund as Subotic has been ruled out for at least six months after suffering ligament damage in Saturday's defeat to Wolfsburg.
The 34-year-old previously worked with Klopp at Mainz, before moving to Bayer Leverkusen in 2007, collecting nine Germany caps and scoring once in his career to date.
Klopp feels the centre back has the qualities to help cover Subotic's injury, noting his "playmaking and athleticism" but insists he is in no rush to make any decisions.
"We have not only lost the game in Wolfsburg, but also Neven Subotic," he told the club's official website.
"With the severity of his injury we had to consider how we deal with it relatively quickly. [Friedrich] brings experience, he has class. Now it's really about how athletic he is.
"He has everything, the good playmaking and athleticism to fit in quickly. But again, it is too early to decide the issue.
"We have all the time available to us to meaningfully respond to the situation of Neven's injury."