The offer was made last month in collaboration with Global Infrastructure Partners and Stonepeak and is said to be at an advanced stage.
KKR has been extremely active with regard to its M&A activity, completing a number of deals last year as it expanded its portfolio.
The investment company has also been interested in Telecom Italia (TIM) although that US$12 billion offer was rejected by the Italian telco.
A final decision has not yet been made according to the report but there are other suitors who are said to be “studying the business” including Vodafone Group.
Canadian investment firm Brookfield Asset Management and Cellnex Telecom also made a bid for part of the Deutsche Telekom asset.
Cellnex is a Spanish wireless infrastructure firm that lays claim to around 53,000 tower sites across Europe and says it is aiming for 137,000 by 2030.
Cellnex already owns towers with Deutsche Telekom in Switzerland and the Netherlands and Germany is the only major European market where it does not yet have a presence.