Spanish striker Morata traded Real Madrid for Chelsea last month for a reported £70million, having also been linked with Manchester United.
Pochettino says Spurs had their eye on the 24-year-old two years ago but he questioned the wisdom of going head to head with Kane, who has been the Premier League's top scorer in the past two seasons.
"Morata talked about myself in the media," said Pochettino.
"He said: 'Mauricio called me'. That was from the beginning, 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?'
"Because it's Harry Kane, I can't compete with Harry Kane or Hugo Lloris or different players."
Pochettino's side are yet to make a summer signing, though they sold right-back Kyle Walker to Manchester City in a lucrative deal.