The Spurs manager is desperate to sign a target man this month after Kane was sidelined with a torn hamstring, which is expected to rule him out until at least April.
Mourinho has shown faith in youth this month, starting 20-year-old academy graduate Japhet Tanganga in the last three matches, but Parrott failed to make the match-day squad in last week's matches against Middlesbrough and Watford, with Lucas Moura and Heung-min Son filling in up-front.
Parrott, who is 18 next month, is a full Republic of Ireland international who has featured in the Carabao Cup and Premier League this season but Mourinho believes the teenager has a long way to go before he can be relied upon to fill Kane's boots.
"I had a long conversation with him today, so I'm ready to share with you a little bit," Mourinho said of Parrott ahead of Wednesday's Premier League clash with Norwich.
"I think he has potential. I think he needs to work a lot. He has a process to go through, a process that probably Tanganga had. One thing is 17 and another thing is 20. We are speaking about three years of distance and three years.
"Ok in Tanganga's case it was three years without a Premier League match, but it was three years or working and playing, playing in his age groups, playing in England national team [youth games], which also gave him some experience. Then with me it was just the last part of his preparation before he had his first opportunity.
"I think Troy has to go through a process. Can he have minutes? Yes, he can. I'm not saying he's not able to have minutes, but to put on his shoulders the responsibility of replacing somebody to be replaced, I don't think he's ready at all."
Edinson Cavani has handed in a transfer request at Paris St.-Germain and Chelsea boss Frank Lampard has refused to rule out a move for the Uruguayan, 32, this month.
Asked if Spurs are interested, Mourinho insisted he would not talk about players from other clubs but joked that he would love France superstar Mbappe on loan.
"[Cavani's] a Paris Saint-Germain player!" Mourinho said. "I think I have a very good relationship with [PSG owner] Mr. Nasser and [sporting director] Mr. Leonardo – I want to keep that great relation, and good relations are based on respect, and I'm not going to talk about a player from Paris Saint-Germain.
"Unless you want to joke – and they are my friends – that they could send Mbappe on loan. More than that I have nothing to say."