Because I grew up being taught about the 4 candidates but in the game Crusader Kings II, in the 1066 start date, King Svend II of Denmark has a strong claim to the English throne. Although he isn't pressing his claim to the throne, obviously. So where does this supposed claim come from? Probably from Canute the Great but.. I don't know.
Svend's (normally Sweyn in English) claim was based on the fact that he was the nephew of Canute the Great (Svend's mother, Estrid Svendsdatter, was Canute's sister) who had ruled England.
And Svend did (sort of) push his claim - in 1069/70 he invaded East England to aid Anglo-Saxon rebels against William. However, Svend ended up accepting payment from William in exchange for his forces withdrawing to Denmark without a fight.
Svend's invasion and subsequent withdrawal were a leading cause of the Harrying of the North.