The agency said the option would continue to monitor food around all licensed nuclear sites but reduce background monitoring away from nuclear sites.
Under the current annual system, samples of food are analysed around all nuclear sites in England and Wales and further background monitoring takes place in England, Wales, Northern Ireland, the Channel Islands and the Isle of Man.
The FSA said the preferred option would bring the UK in line with international best practice and guidance.
The other two options are maintaining the current programme or ceasing radiological monitoring in food and associated reporting.
Closing date for stakeholders to submit their views is 6 March 2013.