The 230,000sq ft Lower Thames Street scheme is just upstream from the Tower of London and will replace the existing Seventies building.
Pace hopes to start the project later this year, if it secures funding.
Sir Robert McAlpine starts out as favourite to take the job having recently finished Riverbank House further along the Thames for Pace.
The proposed new glass-fronted office building was designed by David Walker Architects and is one of the last undeveloped waterfront sites in the City.
Stephen Down managing partner of investment adviser Gresham Down, said: “With City rents rising over the past 12 months by 25% and severe shortage of new office space predicted over the next few years developers are keen to commence new developments, but an absence of finance will mean that only the very best schemes such as Sugar Quay will get started”
For several centuries the site housed Customs officials who monitored and taxed ships and their cargo from across the globe as they sailed up the Thames.
More recently the site has been the headquarters of the sugar company Tate & Lyle as well as quoted hedge fund Man Group.