The Mirror says Haaland has told Solskjaer he wants to sign for United.
The £80million-rated Red Bull Salzburg striker is Europe's most coveted star and his first-choice destination – if he moves in January – would be to Old Trafford.
But his powerful agent Mino Raiola – also Paul Pogba's advisor - is keeping all options open for the hot-shot teenager with Juventus desperate to land the Salzburg star.
Haaland visited the training grounds at Borusssia Dortmund and Red Bull Leipzig last week amid reports that Solskjaer flew to Salzburg on Friday to make a last ditch pitch for the youngster.
Dortmund are pressing hard to sign Haaland but Solskjaer has tried to tempt him to United with the promise of a place in attack alongside Marcus Rashford and Anthony Martial.
It's believed Haaland has already visited United's Carrington training complex and is keen to be part of Solskjaer's revolution at Old Trafford.