The 19-year-old was rewarded with an improved deal earlier this week after impressing for the Red Devils' youth ranks, earning rave reviews since his arrival last year from FC Slovacko.
Kovar has been likened in playing style to United's current number one David de Gea - which could certainly bode well for United in the future - keeping five clean sheets in six games so far this season.
The teenager was even included in Ole Gunnar Solskjaer's squad for the Europa League, giving a further indicator to how much the staff at the club rate the shot-stopper.
His new deal runs until 2023 and is believed to be worth around £15,000-per-week, with the promise of further uplifts if he continues to meet the targets being set.
United do find themselves well stocked in the goalkeeping areas, with Sergio Romero and Lee Grant the established first-team back-ups to De Gea, sparking the wave of interest in Kovar.
It's understood a handful of clubs have asked to be kept updated on the youngster, who rejected West Ham United in favour of a move to Old Trafford in January 2018.
A couple of clubs in League One discussed the likelihood of taking him in the January window, although the Manchester giants are in no rush and may wait until next summer before placing the youngster in the right set-up.
United, however, have already seen how successful loan periods have been for their other goalkeepers, Dean Henderson and Joel Pereira, currently thriving at Sheffield United and Hearts respectively.
Meanwhile, the United first-team squad are currently preparing for their return to Premier League action on Sunday week when they will look to end leaders Liverpool's 100 per cent start to the season.