Kane, 24, has been nominated alongside the likes of heavyweight champion boxer Anthony Joshua, swimming sensation Adam Peaty and Formula 1 champion Lewis Hamilton.
The England international has been given a nomination after winning the Premier League's golden boot award for the second successive season in 2016-17 with 29 strikes, as well as being the only Englishman to be nominated for the Ballon d'Or.
However, ex-Gunner Parlour was quoted by TalkSPORT presenter Alan Brazil's official Twitter account as saying that Kane did not deserve a place among the 12 athletes, as he has not won anything with Tottenham this calendar year.
"He hasn't won the league, he hasn't gone to a World Cup with England got the winning goal or something," Parlour said. "We all know he's a brilliant player, I don't agree with the personality bit anyway. It should be Sports Person of the year.
"It should be what you've achieved in the sport. You can't go against Joshua as favourite, Mo Farah has got a chance." Parlour then asked Brazil: "Would you have Kane on there [shortlist]?" To which Brazil replied: "No."
Tottenham's number 10 has continued his impeccable form this season, scoring 19 goals in 21 games for club and country before joining an elite list of players to score 40 club goals in a calendar year following his strike against West Brom on Saturday.
Now, Kane is expected to be a part of Spurs side as they look to bounce back from their disappointing 1-1 draw against West Brom to beat Leicester City on Tuesday night in the Premier League.