The news of Lord Rogers' interest comes as the Northwest Development Agency considers whether to support a proposal from National Museums Liverpool for a standalone museum at the site.
The agency will consider NML's scheme at a board meeting today , but a decision may be deferred.
NML is part-owner of the waterfront site, next door to the Port of Liverpool Building at the Pier Head. The NWDA owns the remainder, currently occupied by the Road Range car dealership and car park.
NML is hoping the NWDA will support its proposal with £34m of grant funding.
Known as the Museum of Liverpool, their scheme would be one of the largest museums built anywhere in the world for a century.
However Steve Broomhead, chief executive of the NWDA, has warned the agency will not tolerate another Cloud-style debacle. He wants to see that the scheme is economically viable before he will consider putting the agency's name and funds to it.
Doubts have been raised that the proposed content of the Museum of Liverpool will attract sufficient visitors from outside the region to justify major public funding. In total, NML is hoping for £65m of public money from the NWDA and Merseyside's Brussels' funded Objective 1 programme.
It also emerged yesterday that NML has already completed the design work for a standalone museum on its waterfront land.
That work was commissioned last year when it appeared there was strong opposition to NML's involvement in the Fourth Grace project.
NML also has planning permission for the site, initially obtained four years ago and renewed just 18 months ago.