Macca will link up again with former bosses Gerard Houllier and Andy Roxburgh, says the Scottish Sun.
McAllister was No 2 to Houllier at Aston Villa and the Frenchman is Red Bull's global chief.
Roxburgh is sporting director at the MLS side where top stars include where Thierry Henry, Tim Cahill and Juninho.
McAllister said: "It's very flattering to be mentioned in connection with the job, but nothing has been settled.
"But it would be a life-changing opportunity if it happened and it is something that would greatly interest me.
"I have had a couple of approaches in recent months, one from Australia and a couple of projects in the lower leagues in England.
"The game is thriving in the USA. David Beckham did a fantastic job in putting the sport on the map there.
"You see guys like Robbie Keane and Thierry Henry going across and keeping that aspect of it going. I know Robbie has been a real success there.
"New Jersey is a real football hotbed and the standard of the MLS has improved."