Fallon, TBWA\London and the incumbent, DDB London, have been briefed to vie for the task.
At the same time, the MLC is also preparing to take on a roster with the three agencies involved in the pitch expected to be appointed.
The move follows a statutory review of the £2 million account, which was launched in October.
MLC's marketing director, Richard Lowe, is overseeing the project, which comes after a number of changes at the commission.
A shift in accountability recently saw marketing responsibility devolved to the individual regions of England, Scotland and Wales.
As a result, each area now competes against the others for UK customers.
The MLC has faced a tough battle in recent years to increase consumers' confidence in British meat. It put £900,000 into a nationwide campaign following the outbreak of foot-and-mouth disease.