The plans were still at an early stage, but the decision has been taken, the newspaper reported, quoting company sources.
Industry sources put the potential sale price at more than €2.0 billion, the paper added.
A spokesman for E.ON told AFP that "there have long been rumours concerning a possible sale of our Italian activities.
"We're constantly examining the strategic options for optimising our portfolio and this also includes the activities in Italy," he said.
In the past, E.ON invested €11.5 billion in establishing footprints in Spain, France and Italy as part of its ambitions to become one of Europe's biggest players.
But six years after moving into Italy, the profits EON makes there have fallen short of target and the German group is no longer looking to expand in southern Europe, Handelsblatt said.
According to E.ON's website, E.ON Italia has capacity of just over 6.0 gigawatts and is one of the top five in Italy with nearly 1.0 million customers.
Handelsblatt the unit employs a workforce of more than 1,000.