It is claimed two Phoenix players were stopped by police during the early hours of Tuesday morning when spotted driving the cart on a commonly used Sydney road.
One of the players is reported to have been arrested.
Phoenix had been based at an academy in Sydney to avoid quarantine measures upon returning to New Zealand, thus allowing them to play the remaining weeks of the A-League season, but following the competition's suspension on Monday, they returned home the following day.
FFA confirmed knowledge of the reports and insisted it is looking into the allegations, though the identities of the players involved were not revealed.
A statement read: "Football Federation Australia (FFA) has been made aware of a report regarding two Wellington Phoenix players.
"FFA is investigating the matter, which is being taken very seriously. If any misconduct is found to have occurred, FFA will be swift in taking action under the FFA National Code of Conduct.
"FFA is not in a position to comment further at this time."
The A-League is on hiatus indefinitely, though a further formal status assessment is scheduled to take place on 22 April.