Freidrich has been without a club since leaving Bayer Leverkusen at the end of last season, with the 34-year-old having previously worked with Klopp during his time at Mainz 05.
Klopp admitted that with Neven Subotic ruled out for the rest of the season Freidrich is being considered as a replacement, with the main question surrounding his fitness rather than ability to serve as cover.
He told the club's official website: "We have not only lost the game in Wolfsburg, but also Neven Subotic.
"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."
Subotic suffered a cruciate knee ligament tear against Wolfsburg last weekend which will keep him sidelined for at least six months.