The local authority is looking for a sole agency for the four-year framework, which is valued at £1.5m to £2.5m.
Conference Care is the current supplier for the work, which includes venue finding and booking for conferences, meetings and training events.
The new contract is different because it is the first time the framework will be open for use by other authorities, including Hampshire Constabulary, Surrey County Council and members of the Central Buying Consortium.
Hampshire County Council procurement manager Peter Lloyd told C&IT that plans for using just one supplier for the framework were because it was "more cost effective".
"It is certainly an area of expenditure we are focusing in on," said Lloyd. "We are all making better use of our own resources and premises for events and training."
The deadline for the tender is 19 September, and Lloyd added it was unlikely that live pitches would be carried out.