Morata joined the Premier League champions this summer from Real Madrid for £58million, two years after Pochettino tried to tempt the player to Spurs.
However, the Spain international apparently rejected the move because of the presence of Kane at White Hart Lane.
Pochettino, quoted by several newspapers, said: "Morata talked about myself, in the media he said 'Mauricio called me'. That was two years ago or more.
" He said to me: 'Why do you want me if you have Harry Kane? You know, if you go to try to sign a striker, they will say: 'eh gaffer, you want me for what? To be on the bench? I can't compete with Harry Kane or Hugo Lloris or different players.'
"It's so difficult to convince good players to come and then be on the bench. Then the problems start."
Kane has been the Premier League's leading goalscorer for the last two seasons and Chelsea boss Antonio Conte last week said if there was one striker he could sign it would be the 24-year-old England international, who he described as "a complete player".