The Yorkshire born striker reportedly has a £1 million release clause that if activated could see the 26 year-old make the move from Cardiff City to South London.
However Palace will face stiff competition from newly promoted Leicester who are looking to strengthen their attacking options.
Campbell began his career at Manchester United, a product of the academy system Campbell made four appearences before being loaned to Royal Antwerp. After a successfull spell in Belgium that saw the striker net 24 goals in 38 games Campbell made a permanent move north to Sunderland. Campbell's spell at Sunderland was plagued by an anterior cruciate ligament injury that saw the highly rated youngster's playing time limited as he struggled to make match fitness.
On 21 January 2013, Campbell signed for Cardiff City on a three and a half year deal. After helping Cardiff seal promotion to the Premier League, Campell announced himself in England's highest tier with a brace that helped seal a 3-2 victory over the eventual champions Manchester City. Despite being unable to prevent Cardiff from relegation Campbell finished the season on a high as Cardiff's top goalscorer with 9 goals in all competitions.
For a cool £1 million, Campbell could link up with Dwight Gayle and Glen Murray in the Eagle's attack or provide a quality back up option.