Spokesperons for Constable and Christie denied the report to MSNBC. To read the full MSNBC post about the interview, click here.
In a statement, Colin Reed, a press spokesman for Christie, wrote,
"Governor Christie and his entire administration have been helping Hoboken get the help they need after Sandy, with the city already having been approved for nearly $70 million dollars in federal aid and is targeted to get even more when the Obama Administration approves the next rounds of funding. The Governor and Mayor Zimmer have had a productive relationship, with Mayor Zimmer even recently saying she's 'very glad' he's been our Governor. It's very clear partisan politics are at play here as Democratic mayors with a political axe to grind come out of the woodwork and try to get their faces on television."
The allegations are the latest headache for Christie, widely considered to be a contender for the 2016 Republican nomination for president.
(Read more: Feds probe Christie use of Sandy funds: Report)
Last week, it was revealed that top staff in Christie's office were involved in a traffic scandal that snarled traffic around the George Washington Bridge for days.
Following the interview, N.J. State Senator Steve Sweeney issued the following statement:
"The allegations made this morning by Hoboken Mayor Dawn Zimmer on Up with Steve Kornacki are extremely disturbing. We will pursue these assertions to determine if they are true and if they are connected in any way to the actions and practices behind the George Washington Bridge lane closings. The lane closings were an abuse of power. These new revelations suggest a pattern of behavior by the highest ranking members of this administration that is deeply offensive to the people of New Jersey. If true, they could be illegal. There is no place in public service for actions like this or for the people who are responsible."
—By CNBC's Katie Little. Follow her on Twitter