The future of the project was thrown into jeopardy last month when its architect, Richard Rogers Partnership, was sacked by the Welsh finance minister Edwina Hart over claims of spiralling cost.
But developer Grosvenor Waterside, the freeholder for the Cardiff Bay site, told Building that it will "express an interest" in driving the 3300 m2 project forward.
Phillip Williams, managing director of Grosvenor Waterside, said the firm is keen but would have to "explore the parameters" and details of the building before deciding whether to bid.
He added that the developer would like to see the building under construction as soon as possible, so that other developments in Cardiff Bay are not harmed by the delay of the project.
Any move by Grosvenor Waterside would depend on the assembly's seeking a PFI procurement route. This would involve taking on board a developer and then leasing the building from the chosen development company.
At the time of RRP's sacking, Hart hinted this was her preferred route. In a statement to the assembly, she said: "The assembly is therefore being asked to agree to seek proposals from developers to complete the design and construction of the building, either for lease to the assembly or for a lump-sum purchase."
Local architects and design-and-build companies are "keeping their eyes open" for an advertisement to this end in European Union's Official Journal, according to one source.
Despite the likelihood of a new procurement route, the icy relationship between the assembly and RRP finally appears have thawed with an exchange of letters.
Hart wrote to Richard Rogers on 23 July following his comments to the BBC that his company could deliver the project on budget. Hart challenged Rogers to write back with a proposal to back up his claims.
A spokesperson for RRP confirmed that Rogers replied "at the tail end of last week". He said: "Our outlook towards the project is positive. If we can get back on track then we'd like to, but more discussion needs to take place."
A Welsh government source said "nobody is confident" about the outcome of talks between the two.
The Welsh assembly sagaMarch 1998
Cardiff chosen as the home of the Welsh assembly
Nearly 90 architects express interest in designing the building
Richard Rogers Partnership selected by a panel led by Lord Callaghan of Cardiff
First secretary Rhodri Morgan suspends the project, after concerns that the cost had almost doubled to £23m
RRP accused in a report of an escalation in its design fee of £1.4m to £3.4m
RRP sacked over spiralling cost of the project – estimated at more than £40m, at least £13m over budget.