The last time the company increased its director fee pool was in November 2016 when shareholders approved a 33 per cent increase to the current $950,000.
The New Zealand Shareholders Association voted against that proposal and chief executive Michael Midgley says this latest proposal will be closely considered.
"It will be getting careful scrutiny," he said.
a2, which has an eight-strong board, said since the last increase in fees the company's market capitalisation has increased by more than 350 per cent.
Full year revenue and full year basic earnings per share since the 2016 financial year have also increased, by 162 per cent and 514 per cent respectively, it said.
"In the last year, the company has entered into a number of new markets, introduced new products, and enhanced its strategic partnerships, as further reported on in the company's annual results for the 2018 financial year.
a2 has attempted to water down concerns about new laws covering cross-border e-commerce (CBEC) trade into China and the grace period for existing regulation that runs out on December 31.
a2 Milk's chief executive for Asia Pacific, Peter Nathan, recently told the Herald the company's view remained "entirely consistent" with its September announcement and he believed the grace period for new rules would be extended beyond January 1.
Craigs Investment Partners last month downgraded its recommendation on the stock to 'hold' from 'buy' and indicated a target price of $13.50.
In a market presentation last week a2 said its guidance for the full-year results remains unchanged, while providing no actual numbers.
The company reported a $195.7m net profit for the year ended June, up from $90.6m the previous year.
The dual-listed a2 will hold its annual meeting in Melbourne on November 20.