The Spanish international has been linked with a move to the Premier League this January, with Arsenal and Tottenham Hotspur both reportedly interested in his services.
The North London rivals would have been impressed by Negredo's clinical finishing as he found the net in a convincing victory at Ramon Sanchez Pizjuan.
There were few chances for either side in the opening half-hour and it needed a set piece to break the deadlock.
Granada created little going forward but Sevilla could not kill the game off until Negredo emphatically dispatched a Rakitic cross on 70 minutes.
The scoring was complete when Gary Medel, who had earlier left the field to receive treatment on a cut to his head, latched onto a Negredo pass before firing home from 12 yards.
The result sees Sevilla climb to 11th in La Liga, while Granada are just two points clear of the drop in 17th.