Spurs boss Mauricio Pochettino claimed over the summer that the Spain international once turned down the opportunity to move to north London as he was concerned about the presence of a striking rival.
The Argentine coach 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?'"
The 25-year-old maintains that Spurs were never an option for him and has sought to make it clear that he never shunned the opportunity to work with Kane.
He told Sky Sports on Pochettino’s claims: "No it's not true.
"I spoke with him and he said he wanted both [of us] to play together, but there was no chance to come to Tottenham.
"For sure I would like to play with Kane, he's a big player, one of the best strikers in the world, but in this moment when I spoke with him [Pochettino] there was no chance to leave Real Madrid."
Morata has faced his own challenges at Chelsea, with Antonio Conte having acquired him to fill the boots of international team-mate Diego Costa.
"He is a very good player and a good man too. I'm Diego's friend and when I came here I knew that is was a big responsibility to replace him, but I've tried to do well," Morata added.
"Always when we are together in the Spanish team, we talk about football and life. We talk about everything and I always say thanks to Diego."
Morata has netted 12 times in 25 appearances for Chelsea this season and while he is happy with that return, he believes there is still more to come from him.
He said: “I can score more goals. I had many chances in the Premier League and Champions League and I need to improve. It's my first year here but I think I can do better and I need to do that.
"Always I can improve something. I'm not perfect, if there's one thing that I can improve then I try to look for that and work every day to do so."
Morata’s next opportunity to get on the scoresheet could come against Stoke on Saturday, with the Potters set to pay a visit to the defending Premier League champions.