In an all-staff meeting last Thursday, the senior management team made the offer, which staff have since been considering.
Employees were given a week to make up their minds and BBH management will make its final decision on whether or not to implement the measure today (Friday).
Over the past week, the agency has also been offering staff voluntary sabbaticals of up to six weeks in length to take any time this year.
Ben Fennell, the chief executive of BBH, said: "We really don't want to make redundancies but we can't force people to accept these changes. However, these things can often be galvanising for an agency."
In the US, thousands of people have been made redundant because of the recession, while job losses in the UK have been relatively small by comparison.