Pep Guardiola's side have been heavily linked with bringing in a new centre-forward as club-record goalscorer Sergio Aguero is out of contract at the end of the season and options are needed beyond Brazilian Gabriel Jesus.
Kane has previously been linked with a move to the Etihad Stadium, but Agbonlahor believes that the England international would struggle in Man City's all-action system which requires relentlessly pressing.
"I think he could do it [make it at City] but is he able to do the pressing part? We've seen Gabriel Jesus, he doesn't stop. You look at Harry Kane, he's a fantastic goalscorer but is he going to want to do that pressing that Pep is going to demand?" the former Aston Villa striker told talkSPORT.
"[At Tottenham] he knows he can get away with shooting on sight. With Pep there's no way. If you're not making that right pass and being super selfish, you aren't playing under Pep Guardiola."
Kane has scored 22 goals and provided 14 assists across 34 appearances in all competitions so far this campaign, including a strike in the 4-0 victory over Burnley last weekend.