The landmark - to be sited off the Mall in central London - would be located close to an existing statue of King George VI, the Queen Mother's late husband.
Designers only have until the end of the month to submit concepts for the £1.2 million project, which will be funded by the sale of a commemorative coin in 2008.
Expressions of interest will be assessed by a panel on criteria including the quality of the designer's previous work, relevant previous experience, fee and references.
The brief, further details of which can be seen at www.qmmemorial.gov.uk, suggests the use of materials such as Portland stone, granite, bronze and cast iron.
The Crown, organising the contest, also 'discourages the use of water and moving parts' - the source of problems for Gustafson Porter's Princess Diana fountain in Hyde Park - to simplify the memorial's maintenance.