This is one of several plans which will be discussed by members of the controllers' union, the IPMS, at a special conference at Stockport next weekend.
The controllers say the plan will undermine safety and they fear a repetition of what happened to the rail system.
Iain Findlay, IPMS national officer responsible for the controllers, said yesterday that morale was extremely low and that the plans were "getting up the noses of staff".
Other points in the protest are strikes against the National Air Traffic Services' introduction of performance-related pay - and a 10-day training course, which they reject despite an offer of £8,000 for doing it.
The controllers have to be trained to work at a new centre at Swanwick in Hampshire from the beginning of next year. But a shortage of staff means that some would have to give up leave to complete the training in time.
Mr Findlay said there was a 98% vote against the £8,000 among controllers because they were already working too hard.
A Nats spokeswoman said that it had not seen the contents of the resolution and was unable to comment.
The government's plans for a partial privatisation were put on hold last month for three months after being defeated twice in the Lords. Parliament has agreed to the breathing space to allow for further talks.
There are three final bidders: the consortium of seven British airlines, Lockheed Martin and Serco. Ministers have started to press ahead with the plan again, so that it can be in place in March.