Owner CIT bought the building for £60m earlier this year.
The tower, which dates from 1972, has been empty since IPC Media relocated in 2007.
CIT has appointed KPF architects to draw up new plans for refurbishing and extending the existing buildings.
The developer proposes adding six floors to the 31-storey tower, which would be mostly filled with residential accommodation. Around 140 1-, 2- and 3-bedroom homes would be created.
The lower floors of the tower and the podium building would be refurbished but remain as office space.
Kings Reach Tower includes the Milroy Walk shopping precinct, which would be replaced with new retail units facing onto Stamford Street, Rennie Street and Upper Ground.
A planning application is likely to be submitted to Southwark Council in early 2011, with an estimated completion date of mid-2014.