Haaland is expected to leave Borussia Dortmund at the end of the 2021-22 campaign, and a number of leading European clubs, including Man United, are set to battle for his signature.
There had been suggestions that Cristiano Ronaldo's return to Old Trafford would see the Red Devils cool their interest in the Norwegian, but a move is seemingly being planned next year.
According to The Mirror, both Solskjaer and Murtough agree that Haaland should be the club's leading target ahead of next season.
The 21-year-old has again been in excellent form for Dortmund at the start of the new season, scoring 11 times and registering four assists in eight appearances.
In total, Haaland, who played under Solskjaer at Molde, has found the back of the net on 68 occasions in 67 appearances for his current side in all competitions.