The Belgium international scored 25 times in 36 games in the Premier League last season to finish behind Kane following the Englishman’s return of 29 goals in 31 outings.
Lukaku’s prolific form secured a £75m move to Manchester United from Everton in the summer after he opted to move to Old Trafford ahead of a return to Chelsea.
The Belgium international has already scored seven goals in eight games, although the Liverpool defence managed to keep Lukaku quiet last weekend at Anfield.
Kane failed to get on the score sheet in August but the Spurs forward has scored 14 times in 10 games for club and country since his dry spell.
The England international has finished as the Premier League’s top goal-scorer in the last two seasons.
Former Liverpool and Spurs midfielder Murphy believes Kane wants to score more than Lukaku.
“Kane [will finish as top goal-scorer]. He wants it more [than Lukaku]. He wants it more than all of them. He is a goal-scoring machine,” Murphy told Sky Sports.
Kane and his Tottenham team-mates will line up against Liverpool at Wembley in their next Premier League game on Sunday afternoon.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news