The winning agency will be briefed to create a launch campaign that informs people that the Woolworths brand still exists, in addition to directing consumers to the new website.
The work is expected to include TV advertising as well as digital elements.
It is anticipated that the site will launch imminently and it is thought that the pitch will be rapidly concluded.
The high-street retailer, which closed in January, was acquired by Shop Direct last week for an undisclosed sum.
The company, owned by Sir David and Sir Frederick Barclay of the Telegraph Media Group, counts Littlewoods and Choice among its portfolio.