The scheme - which has the financial backing of the Heritage Lottery Fund - forms part of a wider initiative to restore the historic landscape of the Grade II-listed park.
The brief demands that the pavilion should respect both the landscape and the fine Grade I-listed Priory building, which is a scheduled ancient monument.
Councillor Rob Ellingham, the executive member for leisure and community development, said: 'Our aim is to conserve and restore the features, spirit and coherence of a mature 18th-century park; while integrating high-quality public recreational facilities and the Priory building, which functions as a school.
'The park is a facility for the whole community and it is important that local people get involved in deciding its future,' he added. 'We hope that the local community will help us choose the pavillion design for the park.'
The total budget for the pavilion is anticipated to be in the region of £265,000. For a preliminary briefing paper, contact the RIBA Competitions Office on 0113 234 1335 or visit www.ribacompetitions.com.
The expression of interest deadline is Wednesday 2 March 2005.