The Arsenal forward has been linked with a shock £70m switch from north London to Manchester this week.
Aubameyang only joined the Gunners last year but has become a fan-favourite at the Emirates Stadium.
United would make a huge statement should they be able to poach the striker up north, as they did Robin van Persie when Sir Alex Ferguson was in charge.
Emery will no doubt be keen to keep Aubameyang beyond the summer.
But the Spaniard has been told by talkSPORT host Adrian Durham to quit his post at Arsenal if a transfer does materialise between the two Premier League clubs.
“There’s this story about [Aubameyang] allegedly liking a social media post which called Emery a puppet,” Durham said.
“It has fuelled all this speculation even more, but I can’t square this transfer. It doesn’t sit well with me.
“If Aubameyang, having scored all those goals for Arsenal, one of the few bright spots for Arsenal last season, if he went to Man United it would be right up there with the Van Persie thing as a betrayal of the Arsenal fans.
“I think Arsenal fans would look at this and say ‘Hang on a minute we haven’t been forking out money following this club, putting up with mediocrity by their standards for all these years just for us to get a decent strike partnership going and then one of them gets flogged’, to a rival as well.
“I think this deal cannot happen, I think Emery needs to come out and say ‘Right this deal cannot happen and if it does happen, I’m walking out on the club’.
“Something has got to happen to stop the bad decision-making at Arsenal football club.
“This deal, I think, is one of those moments in Arsenal’s history.
“If it happens, then I think the fans will turn massively.”
However, Durham doesn’t believe a transfer will happen.
“I don’t expect Man United to sign him and go on and win the league,” he continued.
“But Arsenal are in a position where they’re rivals to Man United for a top-four place at the very least.
“They’re trying to push on, they’re trying to get better – why on earth would they sell a player like Pierre-Emerick Aubameyang?
“I can’t really get my head around it.”