The process is being handled by the Crown Commercial Service, which is seeking an agency to create a consumer awareness campaign that will raise the number of organ donors.
The activity will be PR-led but also contain digital elements. RFIs have been sent to government roster agencies and are due back by the end of the week.
DLKW Lowe has held the NHS Blood and Transplant blood-donor account for more than 15 years.
The agency created a YouTube ad for Christmas 2013 that encouraged people to give blood at the time of year that it is most needed. The work, "must have gift", helped the service surpass its target by 55 per cent.
DLKW Lowe is not affected by the organ donors pitch.
23red has previously worked with NHS Blood and Transplant and is taking part in the pitch.
In 2009, Abbott Mead Vickers BBDO created the service’s first-ever UK-wide multimedia organ-donation campaign.
NHS Blood and Transplant did not respond to requests for comment.