The British tabloid claims that the 19-year-old winger plans to call on the Olympic sprinter to help him before his pre-season with Newcastle begins.
Aarons has not played a competitive game for the Magpies since November due to hamstring problems, although he has started training with the first team.
It has been reported by The Sun that the youngster will hope to better his fitness by working with 2004 Olympic gold medallist Campbell, who works with sports conditioning firm Back 2 Action, helping footballers improve their sprinting.
Aarons is a highly-rated young footballer who was expected to enjoy a breakthrough season, but injuries have severely impeded his progress.
There is still a chance that the England Under-20 international could return to action before the end of the season, but it is unlikely that he will be able to make a huge impact.
Next season will be huge for Aarons, who will be looking to break into the first team and establish himself as a key player.
The youngster has the talent to make it big in the Premier League; what he needs is to be fully fit.