In 45 appearances for Dortmund, he has netted 43 times and is being chased by almost every elite European club.
ESPN says Solskjaer remains in close contact with his countryman as he looks to convince him that Old Trafford should be his next destination.
The Red Devils coach was asked about the former RB Salzburg star earlier this week and he refused to rule out a move.
Solskjaer had worked with the forward when the two were at Molde but he chose to sign for Borussia Dortmund instead.
Now Haaland's future is under the microscope once again with the 20-year-old continuing his jaw-dropping form.