"I only want to speak to Patrik first before I say anything concrete," the 44-year-old Becker told SID, an AFP subsidiary, having been part of the German team which won the Davis Cup in 1988 and 1989.
He was also Germany's Davis Cup team manager from 1997 until 1999.
Becker won six Grand Slam titles during his career and in 1985 won the Wimbledon title aged just 17.
Having had a public fall out with Germany's top ranked player Philipp Kohlschreiber earlier this year, Kuehnen announced he is stepping down via email on Wednesday.
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"I therefore do not trust the basis for further cooperation and at this point, I end my talks with the DTB about continuing my work.
"I wish the whole team, my successor and the DTB success for the future."
Having beaten Australia 3-2 to stay in the World Group last month, Germany have a tough away match against Argentina from February 1-3 2013 in their next Davis Cup match.
"I understand the decision Patrik has made," Kohlschreiber told SID on Wednesday after he missed the win over Australia because of the disagreement with Kuehnen.
Kuehnen took over from Michael Stich in September 2002 as Germany's captain and his best result was the semi-final defeat to Russia in 2007.
The last time Germany won the Davis Cup title was in 1993 when they beat Australia in the final.