Amorim, having finally received his visa, took his first training session as Man United boss on Monday, and a number of academy players were involved due to the number of first-team stars on international duty.
According to the Manchester Evening News, there was a spot in the session for Kukonki, with the 16-year-old making a huge impression for Man United Under-18s in the early stages of the campaign.
It is the first time that the centre-back has been called up to a senior training session, with Amorim allegedly being made aware of his progress in the opening months of the current campaign.
The 6ft 5in centre-back has made nine appearances for Man United at Under-18s and Under-23s level this term, scoring once and providing one assist in eight appearances in the Under-18s Premier League.
Kukonki trains with Man United in Amorim's first session
Kukonki, who is a left-footed defender, has drawn comparisons with Man United's Josko Gvardiol, with the youngster capable of playing as a left-back as well as a central defender.
Amorim is expected to implement a 3-4-3 system at Man United, which could make it easier for the defender to make the breakthrough over the next year or so.
Man United will gradually welcome back senior players from international duty this week, at which point Kukonki is expected to return to training with the academy, but he is thought to have already made a positive impression.
Amorim is expected to keep a close eye on the Under-18s considering the quality in the squad, with the team currently top of the Under-18s Premier League North, picking up 27 points from nine matches.
Which other Man United Under-18s are likely to be on Amorim's radar?
Man United won the race to sign Chido Obi Martin over the summer after the 16-year-old left Arsenal, and the highly-rated striker has already made a big impression for the Red Devils at Under-18s level.
The forward has scored four goals and registered one assist in four appearances, including a hat trick on his full debut against Nottingham Forest Under-18s at the end of October.
Obi Martin scored 32 goals in 18 appearances for Arsenal Under-18s last season, including 28 goals in his last nine appearances of the campaign, and he is being tipped to become a first-team star at Old Trafford.
Bendito Mantato, meanwhile, has also been in excellent form for the Under-18s this term, scoring six goals and registering one assist in nine appearances, and Amorim allegedly believes that he could be perfect for the right-sided wing-back role at the club.
Amir Ibragimov is also among the biggest talents in the Man United academy, with the attacker scoring five goals and registering two assists in nine appearances for the Under-18s at the start of this season.