The Red Devils are among a host of top European clubs that would like to sign the Borussia Dortmund striker.
But Cole thinks his former club have lost the ability to lure players on reputation alone, with other clubs, like rivals City, surpassing them in recent years.
"To get these guys to come, Haaland for instance, you've got to entice them with something," Cole told The Mirror.
"You've got to entice them with the possibility of winning silverware or being a year away from it.
"If you're playing and have the option of all these clubs, where would United really figure at this moment in time?
"Even though I love United, I don't think the club now can ride on its name alone, especially when you're trying to bring these players in.
"It's not like when I signed for United. We have to be brutally honest, back then everybody wanted to go there.
"We're talking 2021 now. Does everyone want to go to United now? I'm not quite sure everyone wants to now."