Free agent Friedrich training with Dortmund
Subotic has been ruled out for at least six months after suffering ligament damage in Saturday's defeat to Wolfsburg, with coach Jurgen Klopp considering fellow centre-back Friedrich as a replacement.
The pair worked together at Mainz, before Friedrich moved to Bayer Leverkusen in 2007, collecting nine Germany caps and scoring once in his career to date.
Klopp feels the 34-year-old has the qualities to help cover Subotic's injury 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."