City are in the market for a new forward after letting Sergio Aguero join Barcelona on a free transfer.
Kane is reportedly keen to leave Tottenham Hotspur in search of trophies, but they've slapped a £150 million price tag on him.
Sinclair believes that is too much and for £110 million less, he'd rather have a punt on Abraham.
The 23-year-old isn't in Thomas Tuchel's plans at Stamford Bridge despite being their joint top scorer last campaign.
When asked about signing Abraham over Kane, Sinclair told talkSPORT: "I would, yeah.
"He's a young enough player and with Pep Guardiola's coaching ability and the teammates around him... he's a top player.
"The season he had at Aston Villa and then he went back to Chelsea and did very well. He's a handful, his pace, he looks to stretch the lines, he's a finisher.
"No player's perfect, especially at 22 or 23, but there's a lot of growth there with Tammy.
"He'd be someone I'd be very interested to see at Manchester City."
: "I would start Tammy Abraham at #MCFC, he's a top player."- talkSPORT (@talkSPORT) July 26, 2021
:moneybag: : "Would you rather sign Tammy for £40m or Kane for £150m?"
:pencil: : "I would rather sign Tammy!" @Trevor8Sinclair doesn't want to see Man City spend £160m on Harry Kane. :x: pic.twitter.com/lPuOJCrprK
Sinclair admits that it's an unlikely transfer given Abraham's current status, with Arsenal and West Ham United linked.
He continued on Kane's price tag with: "It just goes against my principles of what I think about the club. Honestly, it really does.
"I just don't want to see the club going out there and spending that ridiculous amount of money to bring one player in. That just kills it then. You might as well pack up."
A report from the Sun last week claimed Kane had been given the greenlight to join City by Spurs chairman Daniel Levy.
Any deal involving the England captain would smash the current British transfer record, which saw Paul Pogba join Manchester United from Juventus for £89 million in 2016.
The 28-year-old would likely become the highest earner in the entire league in addition to that.
Who do you think Manchester City should sign this summer?
Let us know in the comments.
Featured Image Credit: PA Images
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