We profile three men who've played for both clubs.
Norwegian goalkeeper Thomas Myhre got his break in English football with Everton after impressing for Norwegian Tippeligaen side Viking in 1997.
Myhre made 82 appearances for the Toffees before moving to Turkish side Besiktas in 2001.
After a year in Turkey, Myhre joined Sunderland in 2002 and played 40 times during his time on Wearside, proving an able replacement for Thomas Sorensen as the Black Cats returned to the Premier League.
He left Sunderland in 2005 and spent time with Charlton Athletic before returning to Viking prior to his retirement in 2011.
French striker Louis Saha started his career with Metz after joining from the famous Clairefontaine football academy.
He impressed with the French side prompting his fellow Frenchman Jean Tigana to bring him to Fulham in 2000.
He scored 63 goals in his time at Craven Cottage, form that earned him a £12m move to Manchester United in 2004.
Despite his time at Old Trafford being plagued with injuries, Saha still scored 42 times in all competitions for United before leaving for Everton in 2008.
The French international played over 100 times for the Toffees before moving to Tottenham Hotspur and the Sunderland in 2012.
Injuries affected Saha’s time on Wearside restricting him to just 14 appearances before he joined Lazio in 2013.
Gateshead-born Don Hutchison started his career with Hartlepool before moving to Liverpool in 1990 under Kenny Dalglish.
He spent four years at Anfield before Harry Redknapp signed the Scottish international for West Ham United in 1994.
Hutchison signed for Sheffield United in 1996 and impressed under Howard Kendall before following his boss to the Toffees in 1998.
After two years at Goodison Park, Hutchison joined Sunderland and played 37 times in his sole season with the club as West Ham broke their record transfer fee to bring him back to Upton Park.