The NAS shifted its headquarters to the west 15 years ago and a move east will inevitably raise prospects of an informal alliance with the Scottish Secondary Teachers' Association and the Professional Association of Teachers.
The second largest union in Britain currently boasts 170,000 full-time teachers, with around 3,500 north of the border. It is the smallest teaching union in Scotland but is keen to use its national muscle to attract new members.
Carol Fox, Scottish official, said: "A move to Edinburgh will place us closer to other teacher unions and would enable us to explore further possibilities. There has to be a strong and independent voice for Scottish teachers."
Jim Docherty, the SSTA's assistant secretary, said: "We have no objections to any super, giant Scottish teachers' union based on a federal structure but there would be no chance of a takeover."
The last approach from the Educational Institute of Scotland was rebuffed on this issue.