Allen, who represented Spurs between 1984 and 1988, registered 49 goals across the 1986/87 season a tally no player has come near to surpassing ever since.
However, the 56-year-old feels given Kane’s growing stature in front of goal, it’s a matter of when not if the current England international breaks it.
“The 86-87 season was a phenomenal season for me and one I’ll never forget,” he said, as reported by football.london.
“Whether or not anyone beats it…I’ll be honest, I hope they don’t! But if anyone can, it will be Harry, for sure.
“I grew up listening to my father Les (striker in Spurs’ double-winning team of 1960-61) and Jimmy Greaves took his place in the double side. He told me he was the greatest goalscorer that’s ever been.
“I managed to beat his best total and I’m proud of that, and I see great things in Harry. It’s absolutely fantastic what he’s done.
“Don’t forget after that first season in 2014-15 people were saying ‘well, it was a bit of a lucky season, a one-off’ but he’s now done it for three seasons, not one. To be that consistent at that level is phenomenal, especially in the modern game now.
“He’s in the best place to score goals – so anything is possible!”
Kane, a graduate of Spurs’ academy, ended the season just gone having managed 35 goals across 38 matches in all competitions.
It was the 23-year-old’s best return since establishing himself as a regular Spurs first team player in 2014.
He also won back-to-back Premier League golden boots, despite missing a chunk of the season through injury, as well as becoming the fourth player in league history – after Alan Shearer, Thierry Henry and Ruud van Nistelrooy – to notch 20 goals in three consecutive seasons.
Heading into 2017/18 campaign the London-born marksman has 99 goals for Spurs to his name which leaves him 24 behind from entering the club’s all-time top 10 which is headed by the legendary Jimmy Greaves (266 goals).