The offer was not enough for the Wellington-headquartered company to recommend it to its shareholders, but the Z board did approve a four-week period of exclusive negotiations.
Analysts warned the process could include a protracted regulatory process, with the sale likely to require Ampol to sell its existing New Zealand business, Gull.
Z Energy chief executive Mike Bennetts said at the time that the period would allow it time to seek feedback from its shareholders and consider the nature of Ampol's offer.
The non-binding offer proposed restricting dividend payments while the takeover process was underway, with Z Energy appearing to believe regulatory clearance may take longer than Ampol did.
Reports from across the Tasman suggested the ability for Z to continue to pay dividends if the sale process dragged on had emerged as a sticking point.
After the offer was announced, some analysts predicted a rival buyer could energy, forcing up the sales price, however the extension of the Ampol process suggests no other serious rivals are circling.
Z Energy's statement was brief, saying shareholders would be updated by October 11, the new deadline for the exclusivity period ends.
"There is no certainty that discussions between Z and Ampol will result in any agreement on a transaction. The board will continue to keep shareholders and the market informed of material developments."