The Spanish-owned energy supplier is holding the review through Creativebrief.
Carat Edinburgh is the incumbent and has handled the business for more than 14 years.
In August last year, Scottish Power called a review of its advertising business held by the Edinburgh-based Newhaven.
The review, also handled by Creativebrief, is expected to conclude in the next two weeks.
Earlier this year, the company appointed Glue Isobar to its digital account after a review that began in September last year.
Scottish Power’s advertising and media reviews are part of the utility’s attempts to become a truly national consumer brand.
Until now, it has advertised primarily across Scotland and North-West England. However, Scottish Power will soon start advertising across the UK.