Planning officers at Westminster Council described the scheme as "acceptable in heritage terms", suggesting that it would secure crucial investment in the London landmark.
But questions were raised about the proposal's ability to meet the minimum social housing contribution, reported the Times.
Prime Investors Capital (PIC),whi ch bought the former government building last year on a 99-year lease for £60m, has offered to make a payment of £700,000, of which £600,000 would be for social housing to be developed elsewhere in the borough. The rest would be for public art.
However Westminster's planning officers challenged the acceptability of the £700,000 figure in a report published ahead of a committee meeting next week. It is thought likely the council will push for a higher contribution.
A members' club that will form part of the development was also questioned by the council, which suggested that its capacity should be limited to 300 people, rather than the 400 proposed by PIC.
A Westminster City Council spokesman said: "The planning committee will look at the application next Tuesday, before making a decision on what is an important building in an iconic part of the capital."
Earlier this year, we reported that a luxury hotel operator was being sought for the Admiralty Arch following speculation that it might be run by the fashion designer Giorgio Armani.