The Tottenham Hotspur attacker failed to find the back of the net in the group stage for England, despite the Three Lions coming up with a joint-high nine goals against Iran, Wales and the USA.
Kane ended his goalless streak with a clinical finish against Senegal in the last 16, collecting the ball from Phil Foden after a quick counter-attack and firing home past Edouard Mendy.
The 29-year-old now sits on an impressive 52 goals for his country, level with all-time women's goalscorer Ellen White and just one behind Rooney's record of 53.
Kane therefore needs just one more goal to equal Rooney's long-standing record against France, and a brace would see him dethrone the Manchester United legend at the summit.
Kane's 52nd goal for England came in his 79th cap, and the striker also has 17 assists to boast at senior international level, three of which have come at the current World Cup.
Prior to the 2022 tournament, Kane had netted 10 times at major international tournaments for England, level with Gary Lineker, who scored all of his 10 strikes at the World Cup.
However, Kane's strike against Senegal made it a record 11 major tournament goals for the England skipper, who has seven to his name at the World Cup and a further four at the Euros.
While the Tottenham man is out to equal or set a new individual record, Gareth Southgate's side have already matched a national goalscoring record during their prolific showings so far.
England have already scored 12 goals in their four World Cup matches so far, hitting Iran for six before putting three past Wales and Senegal in successive matches.
In doing so, the current Three Lions crop have equalled the record for most goals scored at a major tournament for England, who also notched up 12 strikes at the 2018 World Cup.
England manager Southgate is blessed with a fully-fit 25-man squad as his side try to eliminate the champions, with Chelsea's Raheem Sterling rejoining his teammates for training on Friday.
The 28-year-old left the camp after a break-in at his Surrey home last weekend, and Southgate has admitted that he will need to assess the forward before making a call on his involvement.
West Ham United midfielder Declan Rice has also recovered from an illness, while Callum Wilson appears to have shaken off a muscular strain to make himself available.
As a result, England's only absentee for the quarter-final is Arsenal's Ben White, who is not expected to return to Qatar after leaving the camp for personal reasons last week.