The pandemic has brought English football to a standstill and Bullingham said the lack of international matches and FA Cup games will cost the country's soccer governing body around £100 million.
"In the spirit of those on higher salaries taking the greater responsibility, the senior management team have agreed to cut their pay by 15%, with the highest earners in the organisation agreeing to reduce their pay by up to 30%," Bullingham said in a statement on the FA website.
"We are proposing that all employees earning £50,000 or more per annum will take a temporary pay reduction of 7.5%," he said, adding that the FA could lose more than £150 million in revenue if the situation does not stabilise soon.
"We're also looking into what options are available to us through the government's furlough scheme as a contingency plan while we continue to plan for the return of football, once it is safe to do so."
The Times reported that Southgate would take a wage cut of 225,000 pounds over the next three months, while England Women's team manager Phil Neville and the men's England under-21 manager Aidy Boothroyd will take reductions in the region of 15-30%.
The FA decision contrasts with the approach of some Premier League clubs, such as league leaders Liverpool, who said they would be using the government's job retention scheme to pay some non-playing staff who are furloughed.
Tottenham Hotspur, Newcastle United and Norwich City have taken similar decisions, sparking criticism from the government who have taken a dim view of millionaire players and managers not taking wage cuts while the league is suspended.