The company has already approached at least eight full-service agencies in the UK in regard to the pitch.
The winning agency will be awarded the business for an 18-month period, during which time Stanley plans to spend about ú2m on marketing and PR across five undisclosed European countries.
The brief, which is being handled directly by Stanley Tools, is being led out of the company's US offices, with the UK agency expected to work alongside the company's US shops.
Separate campaigns will run later this year targeting the professional and consumer markets, with a focus on the UK.
Stanley Tools' last major campaign, which ran at the end of last year, was intended to boost sales ahead of the Christmas period.
The ú2.4m activity, created by StarNaked Communications, comprised in-store activity, leaflets and specially designed floor units to promote its range. The drive, entitled 'X-Rated', offered consumers the chance to win 'filthy' prizes such as a rally weekend.
Stanley's decision to boost its marketing activity has been prompted by intense competition from DIY stores in the UK, such as B&Q, which now sell own-brand hardware and tools.
In April, Stanley Tools' parent company The Stanley Works announced its first-quarter profits had fallen by 43% year on year.
Stanley Tools operates in the US, Europe, Central and South America, the Middle East, South Africa and Asia Pacific. It has more than 17,600 employees worldwide, with global sales of $3.3bn (ú1.7bn).