Robinson believes Calvert-Lewin is capable of replacing the want away Spurs superstar.
Kane is said to be willing to move away from the Tottenham Hotspur Stadium this summer in search of a club which can match his ambition.
Many big clubs in Europe are interested in signing the England international but Manchester City are reportedly close to agreeing a deal with the 27-year-old.
Robinson, who played for Tottenham Hotspur 2004 and 2008, has urged the Londoners to poach Calvert-Lewin as a potential replacement for Kane.
“If Tottenham lose Kane they need to go after somebody like Calvert-Lewin. He is a player who can lead the line,” Robinson told Football Insider.
“Spurs will have to invest heavily in a number nine if Kane goes. They will have to go deep into their pockets to find a replacement, that’s for sure.
“Go and test Everton’s resolve. Go and put in a massive bid because Calvert-Lewin is someone who I think is capable of taking over from Kane.”
Kane has established himself as one of the best strikers in the world since graduating from the Tottenham Hotspur academy.
He has since scored 221 goals and provided 47 assists in 336 appearances in all competitions for Spurs.
The former Leicester City loanee ended the 2020/2021 season with 23 goals and 14 assists as he won both the Golden boot and best playmaker of the season.