The 38-year-old, whose Gunners contract expires at the end of the season, is only interested in a short-term agreement with Dortmund because he wants to be a free agent in the summer.
With Euro 2008 on the horizon, Lehmann is desperate for first-team football to hold on to the number one jersey in Germany's national team for what is likely to be his swansong tournament.
Lehmann is also thought to be reluctant to uproot his family from their London home, and is seeking a compromise that will cause minimal disruption.
He admitted on Wednesday he is unwilling to commit to Dortmund beyond the end of the season in an effort to allow himself "complete freedom" over his future plans.
"If I can get my private matters satisfactorily resolved then I could come, otherwise I won't," Lehmann told kicker magazine. "If I come to Dortmund then it would only be for six months.
"I want to have complete freedom to decide what I do next in the summer."