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.
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.”