The planning and buying review is being managed directly by the company, and agencies have been asked to submit RFPs. E.ON expects to make an appointment by the end of the year.
MediaCom currently handles the £8.5 million business in the UK.
Earlier this year, E.ON consolidated its advertising and CRM activity in the UK into Engine after a review run by ISBA.
The account is being led by the Engine agency Partners Andrews Aldridge.
DLKW Lowe was the incumbent on the creative business and did not repitch. Havas EHS previously handled the direct account.
Last month, E.ON reported a £182 million drop in turnover for the first half of the year, which it attributed to decreasing standard gas prices in January.
A spokeswoman for E.ON said: "E.ON has an established procurement process in place and, as part of this, we’re tendering for an international media agency.
"We intend to appoint an agency towards the end of 2015 and will not comment further on the process until then."
E.ON was created in 2000 following the merger of Veba and Viag, two of Germany’s biggest industrial groups.