The meeting comes at a critical time for the institute, following six offers to take on the collection and a drive to leave its central London headquarters.
The committee - LI vice-president Jo Watkins, council member Noel Farrer and past president David Jarvis - will discuss the arguments surrounding the library and archive and report to the LI council, which will make a final decision.
However, chief executive Alastair McCapra told HW the aim was not to move with the library once the LI vacates its premises.
Talks are underway with the LI's landlord to attempt to reduce the rent increase. A new tenant then needs to be found so the LI can be released from its 10-year tenancy agreement.
"We are hoping to move as soon as possible, and I want to move into a serviced office and not take the library with me," explained McCapra.
"If we are taking the library with us we will have considerable expense and limit our choices. At the moment we have only looked at space in London."
The archive service is currently suspended, following the redundancy of former archivist Annabel Downs earlier this year.
Land Use Consultants principal Dominic Cole, who has been lobbying the LI to retain the library and archive, explained: "The frustration is that because of the way things have been handled there is now a bias towards disposal rather than retaining the collection in-house."
National Monuments Record head of archives Mike Evans said he had offered his support to the institute: "Our remit is a national archive for the historic environment and historic landscapes are part of that."
But McCapra said the body is now over the worst of its financial crisis, which saw budget cuts spiral to £900,000 earlier this year.
Subscription rates have now been increased by around 9.5 per cent, which is expected to raise £73,000, with £20,000 already raised from early payers.
McCapra said: "It means that a lot of members, however they feel about the situation, are doing their bit to help us get through it."
In addition, a £160,000 loan and a £60,000 overdraft have also been raised using LI-owned premises at London's Barnard Mews as collateral.
"We have done what we needed to do, which was to cut costs quickly and drastically," said McCapra.
"That has put us on a firm footing for the future."