The 19-year-old has been a revelation for RB Salzburg this season when firing home 15 goals in 12 appearances and he has shot to the top of United's wanted list.
Reports have suggested that United will open talks with the Austrian outfit in the January transfer window with a view to doing a deal, but they could be much further down the line with the transfer.
It has been claimed the player's dad, former Manchester City and Leeds United star Alfe-Inge Haaland, has already been to check out United's facilities at Carrington to see what his son could expect.
It would suggest that despite interest from a number of Europe's big guns, the young striker is leaning towards a move to Old Trafford.
The fact that fellow Norwegian Ole Gunnar Solskjaer remains at the helm for United is also a big plus point for the youngster.
Haaland is said to be keen on a switch to the Premier League over anywhere else, but there is also interest from Liverpool and possibly Arsenal.
However, United have nipped in first and will be hoping to get a deal done as soon as possible.
Salzburg are reluctant to sell in the January transfer window, but United hope to get round that issue by offering to loan him back for the rest of the season.
United were heavily criticised for allowing Romelu Lukaku to leave before bringing in a replacement during the summer and someone is needed to provide back up to the likes of Marcus Rashford, Mason Greenwood and Anthony Martial.
Haaland could be the man but the club's fans could have to wait until next season before seeing him in the red of United.