The move comes shortly after FLACQ architects - formed by four ex-Rogers employees - announced plans to revamp the interior of the building.
The practice is also proposing potentially dramatic measures to overhaul the landmark's entrances.
FLACQ's involvement in the project comes after Gensler was quietly dropped in January 2005.
C20 director Catherine Croft is in the process of drawing up a list of backers - likely to include a string of big-name architects - for the campaign to win listing.
She said: 'It's been one of those buildings that everyone assumed would be listed as soon as it was threatened.
'It's been one of those landmarks that has been universally acclaimed for taking architectural discourse forward.'
FLACQ has been working closely on the project with both Rogers himself and the Rogers expert Kenneth Powell.
The London-based firm has won the commission to upgrade the building's underwriting room, the well-known architectural and social focal point of the building, known only as 'The Room'.
FLACQ's Marcus Lee, who is working on new proposals with fellow director Hal Currey, worked on the original building with Rogers and is known to be sensitive to the peer's wishes for the future of the landmark.
He has even claimed that his proposals - largely focusing on the building's interior - would be unaffected by any attempt to get the building listed.
For a special feature on the future of the Lloyd's Building, see today's AJ.