The £56.7 million project aims to extend the facility and turn it into a national museum of textile and design.
The council has set aside £15m for the development and a previous £15m funding bid with Heritage Lottery Fund (HLF) was unsuccessful earlier this year.
However, councillors will be asked later this week to approve a fresh application to HLF and the creation of a project team to continue development work.
If successful, members will begin working on a new funding submission to go to HLF in December.
-- Advertisement --
Council Leader Mark Macmillan said: "While we were disappointed not to be funded first time around, we are certainly not disheartened as HLF made clear it was an extremely competitive round of funding and it is often the case projects like this are not successful on the first go.
"It was encouraging that HLF spoke so highly of what we are trying to do and the benefits it would bring to Renfrewshire - and we now have a clearer idea of what we need to do to be successfully funded at a later date.
"Part of that is further development of the museum's fundraising strategy and we will be pushing ahead with that over the next six months.
"This project could have an utterly massive economic impact on Renfrewshire, creating new jobs, bringing large numbers of day-trippers and tourists into the area, and creating new footfall for Paisley High Street."
Alongside the project, work is underway to create a publicly-accessible museum store in a vacant unit on Paisley's High Street for next year.
The museum attraction is due to be open for 2021.
(LM/MH)
