Kane scored 41 goals in 48 club appearances in 2017/18 and has emerged as one of the world’s best centre-forwards since fully breaking into the Tottenham team in 2014.
The 24-year-old was was vying for a chance in the first-team when Pavlyuchenko was still at the club.
Before leaving for Lokamotiv Moscow in January 2012, the Russian scored 42 goals in 113 games for Spurs across all competitions.
And Pavlyuchenko believes Kane, who is set to captain England at the World Cup this summer, must consider a move to Barcelona or Real Madrid to further his career.
“If Barcelona and Real Madrid call him, then yes, he has to go,” he told Goal. “But if it’s to join a team that occupies the middle of the table in Spain or Italy, it’s not worth it.
“But, he must first know what he wants. It is certain that, if Barca and Real are present, then it’s normal to want to go there.
“Tottenham is a big club, but they don’t play in the final stages of the Champions League. If he wants to go even further, he must, of course, join a bigger club.”
“Today, as you can see, he scores a lot of goals. Many clubs want him and for that I can only say ‘well done’.
“I look at him and see how effective he is. This pleases me, especially since I was at his side during the first steps. I am very happy for him. He is a great Tottenham player today.”
Kane’s season in numbers
In 2017/18, Kane became the first player to score 10+ strong-foot goals (13 with his right foot), 10+ weak-foot goals (10 with his left foot) and 5+ headers (6) in a single Premier League season.
The other was, of course, the contentious goal he claimed touched his shoulder against Stoke City.
Kane also broke a record previously set by Alan Shearer, scoring 39 Premier League goals in a single Premier League year – he sealed the milestone with a hat-trick against Southampton on Boxing Day.
England will be hoping Kane can take his club form into the World Cup finals.