The five-figure brief is for media relations work for Ziering Medical Worldwide, a US company that treats men and women, and founded by surgeon Craig Ziering.
The company, which is launching its services in the UK in February, is understood to be looking for press coverage in the national trade and health media, alongside celebrity patient endorsement.
The brand is currently endorsed by Dancing on Ice judge and This Morning style consultant Jason Gardiner and it is understood another celebrity ambassador is to be revealed.
A spokeswoman for the company confirmed the pitch and that it had been meeting with a number of agencies.
About 30% of 30-year-old men and 50% of 50-year-old men suffer from premature baldness in the UK, while 50% of women experience some degree of hair loss.