Kane was linked with a move to Manchester several times in his Spurs career - after failing to win a major trophy in North London - before eventually opting to join Bayern Munich in 2023.
The England captain has gone on to lift two Bundesliga trophies in Bavaria and he's among the favourites to win the 2026 Ballon d'Or - but it could have been very different for the 33-year-old forward.
"I think he was at a point in his career where he wanted to go and win trophies," Walker told talkSPORT.
"That was the one cloud over his head. He's a great player and had got all these personal accolades for himself, but he'd never won anything for a club.
"He told me 'I want to come,' and was asking me a little bit about it. But, I guess the clubs couldn't reach an agreement."
After the 2021 summer transfer window closed, former City boss Pep Guardiola revealed the club had made four bids to sign Kane, but Spurs turned all of them down.