The chancellor, Sajid Javid, has asked officials to consider whether it will be possible to produce the coins in volume ready for the UK's scheduled EU leaving date of 31 October, the Sunday Telegraph says.
Former chancellor Philip Hammond had planned a limited edition of 10,000 commemorative coins to be sold to collectors for £10 each.
Mr Javid's revised proposal for the coins to be produced for mass circulation is being seen as a statement of intent that the Treasury is committed to Brexit.
It is in contrast to Mr Hammond who angered Brexiteers with his warning about the likely economic impact of leaving the EU and his opposition to a no deal.
The coins will still carry the words "Friendship with all nations" but will be stamped with the new departure date of 31 October 2019.
The Telegraph reported one possible snag could be that the new coin has to be signed off by a meeting of the Queen's Privy Council of ministers, which is not due to meet again until October.