Kane, who has demanded an exit from his club Tottenham Hotspur, is City's main target for the striker position this summer.
But instead of paying the mooted £150 million fee for Kane, Sinclair would rather see a third of that money spent on Abraham, who is out of favor at Chelsea.
Asked about Abraham, he told talkSPORT: "I would, yeah [take him over Kane].
"He's a young enough player and with Pep Guardiola's coaching ability and the teammates around him… he's a top player.
"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."
On the Kane situation, he added: "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."
He finished: "I would like to see Tammy at the club. I don't think it's going to happen because I don't think Manchester City have shown any kind of interest in him. But for me, he's a top player.
"I'd love to see him at West Ham, he'd fit in really well. [Michail] Antonio needs that rest, he can't play week in, week out.
"His age and what he brings to the table, if he puts it all out there one week and then Tammy comes in and plays the next week, that could be a formidable partnership."
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