The 17-year-old was included in a first-team squad for the first time against Arsenal on December 4.
After the match, Amorim noted that the youngster had "impressed" him and demonstrated noticeable maturity.
"He's 16," Amorim told MUTV. "But he impressed me a lot, so it's also a sign to the youth players that they can be here.
"If something happened with the first-team squad, they have to step up, and I think he's ready. He's very adult to handle the demands of the Premier League."
The highly regarded left-footed centre-back was part of United's post-season tour travelling squad in May, making appearances from the bench against ASEAN All-Stars and Hong Kong.
When Amorim conducted his inaugural training session at Carrington in November following his appointment from Sporting Lisbon, Kukonki made a significant impression.
The teenage sensation was then selected to travel to Portman Road for Amorim's debut match against Ipswich Town, but was not in the matchday squad.
He was subsequently named on the bench at the Emirates Stadium as United visited Arsenal and remained around the senior squad for the rest of the season.
Kukonki continued to knock on the door of a debut and was included in the squad for both legs against Lyon in the Europa League quarter-finals.
His performances have earned him his first professional contract, and he has been tipped for a bright future at Old Trafford.
Early comparisons have been drawn to Manchester City defender Josko Gvardiol, with Kukonki offering a unique option as a left-footed defender.
Kukonki, already a towering figure at 6ft 5in, is using his physicality to push towards his ultimate goal of making his debut, having progressed through the youth ranks.
Born in Stoke-on-Trent, he also has experience playing as a left-back and has represented England's Under-17s.