Norwegian superstar Haaland completed his move to Manchester City on Monday, while Uruguayan international Nunez is expected to finalise a move to Liverpool from Benfica in the coming days for a fee that could rise to 100 million euros ($105 million, £85 million).
Kane was keen for a move to City himself last summer, but now looks committed to another season at Spurs after they secured a return to the Champions League.
“Every season I’ve been playing it’s always been a tough battle to win that golden boot,” said Kane, who has won the award for the Premier League’s top goalscorer three times.
“You expect the top strikers to want to play in the Premier League. With those two new signings, that’s going to be the case.
Last season, his Tottenham strike partner Son Heung-min shared the award with Liverpool’s Mo Salah, with both scoring 23 goals.
“It helps me as a player to have good competition, it drives me to improve. I look forward to the challenge,” said Kane
Kane is just three goals off Wayne Rooney’s goalscoring record of 53 for England and reaching his half century against Germany last week.
However, Kane’s penalty in a 1-1 draw in Munich is the only goal the Three Lions have scored in a winless start to their Nations League campaign after three games.
Gareth Southgate has voiced his concern over his side’s reliance on Kane and Raheem Sterling for goals with the World Cup in Qatar just five months away.
And Kane urged his teammates to show more hunger to get on the scoresheet.
“In any top team, you’re going to probably have a main striker that gets the majority of the goals, a main attacking winger who is going to get some goals,” he added.
“I’m sure every lad that puts on an England shirt wants to score and get assists and affect the game.
“The most important thing is the mentality of having that hunger to go and get those goals.”