The Portugese, who took over as Tottenham coach last week, hours after the dismissal of Mauricio Pochettino, said: "I have more than a connection [with Ibrahimovic]. Amazing player, amazing guy, but I would say no chance.
"We have the best striker in England. It doesn't make any sense for a striker of Zlatan's dimension to come to a club where we have Harry Kane."
Mourinho coached Ibrahimovic at Inter Milan and Manchester United, where the former Sweden international played before joining MLS side LA Galaxy in 2018. Ibrahimovic left the club earlier this month.
Speaking at a news conference ahead of his side's Champions League clash with Olympiakos on Tuesday, Mourinho was full of praise for his new squad, and while he said he was optimistic about their chances in this year's edition of the tournament, he said patience was needed.
"With these boys I will never be afraid of any Champions League match," Mourinho said.
"[But] we have to qualify [for the knockout phase] first, that is our focus ... It's only when my teams arrive in the quarterfinals that I start thinking that we have a chance -- in this moment we are far from it.
"Give me time, give me time to develop my ideas and we will have no problem going to play any team in Europe. We are not afraid of anyone."
Pochettino's Spurs side finished runners-up to Liverpool in the Champions League last season after the Argentine said that winning the competition would be a "miracle."
But two-time winner Mourinho said such a feat was more achievable than Pochettino had suggested.
"I change miracle to very hard," the 56-year-old said.
"If Mauricio says that [losing the final affected the players] then he's been here and he's sharing his feelings. It's like landing on the moon, but you don't do it. Look at Liverpool had the frustration of not winning and then the next season they reached the final and won it."
Tottenham earned a 3-2 win away at London rivals West Ham on Saturday in Mourinho's first game in charge of the north London club after succeeding Pochettino, to whom Mourinho said he has not reached out.
"I haven't spoken to him," Mourinho said. "I've been there and I know what he's going through. I spoke to his son, in our academy, and I will call him.
"I told the players here to tell him he's free to come here whenever, to have a meal with the players. If he wants me here or not, that's fine."