Iberdrola, Scottish Power’s parent, is also looking for a shop for activity in Spain.
The process is being handled by Creativebrief. It is understood that UK agencies vying for the work were briefed this week and pitches will take place in June.
Fallon is the incumbent on the UK ad business. It won the £7 million account in July 2013, beating Inferno, MBA and Newhaven in a process led by Creativebrief.
In June 2014, Scottish Power handed its £10 million media business to the7stars, which beat Arena, Carat Edinburgh and UM London.
The incumbent was Carat Edinburgh, which had held the account for more than 14 years. Creativebrief also supported that process.
In August 2014, Rapp landed the company’s consolidated UK direct marketing business.
The appointment formed part of Scottish Power’s strategy to become a national consumer brand. Bright Blue Day previously worked on the majority of Scottish Power’s direct activity.
A spokesman for Scottish Power said: "We don’t comment on agency speculation."