FTI, now based at the State Library of WA, left the Adelaide Street building last May after the City announced it would be doing renovation works on the ageing building.
As part of the move, the City gave FTI the first right of refusal to take up a new lease once the renovations were finished.
However, in last month�s strategic and general services committee agenda, the City said there were indications FTI would not take up the offer.
Fremantle economic development and marketing manager Tom Griffiths said the City had received a number of requests from other organisations eager to use the building and had come up with a plan B in case FTI decided not to return.
�The requests for the use of the building vary between commercial and community purposes,� he said.
�It is important that the City selects a tenant that will have a positive social and economic impact in the area and respects the historical significance of the building following the completion of renovation works early next year.
�We will assess each proposal against the criteria, which has been developed with our strategic plan in mind.�
Renovation works will continue throughout the year, with the roof replacement expected to be finished by September.
Mr Griffiths said while works to the building�s interior would continue until 2018, he expected a tenant be able to move in by mid-2016.