WBN contacted the Duco Events promoter on Wednesday morning following reports a deal was possibly set to be made official between the pair.
Higgins stated Parker has more than one option available to him and is yet to make a decision on which way to go.
“Contrary to media reports, a fight between Joseph Parker and Bryant Jennings has not been confirmed,” Higgins told World Boxing News in a text message before sending out the quotes as an official statement.
“Whilst we are in negotiations with the Jennings camp, we have other options on the table, including Alexander Ustinov.
“No deal will be made on the next fight until Joseph and his team are satisfied with the final terms and a contract has been fully negotiated and signed.
“We won’t be making any further comment for now,” he added.
Should Parker face Jennings, the New Zealander would be looking at a first fight in the United States for some four years. An alternative battle with Ustinov would probably take place on the former WBO heavyweight champion’s home soil.
The Kiwi is aiming to return to form following a points loss to Anthony Joshua, where Parker became the first man to go the distance with the current four-belt divisional ruler.
A Jennings encounter would give Parker the opportunity to begin building his reputation on US soil following on from the Joshua fight, which was aired live and exclusively on Showtime.
More will be revealed in the coming days.
Phil Jay is Editor of World Boxing News. Follow on Twitter @PhilDJay