Mauricio Pochettino has been linked with the hotseat at St. James' Park as Bruce's job looks in doubt amid the imminent arrival of Mohammed bin Salman as the club's new owner.
"I think we have to keep Steve Bruce. He's a good manager and coach, so I think he should stay," Asprilla told Sky Sports News.
"He knows the club well. He's done very good things with limited resources in recent times, so I think he'll be able to achieve more than he has so far with better players at his disposal.
"All the coaches are good and the players are good. I have no doubts about that.
"I think we have to keep him in his role so that he keeps working on this big project."