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Haaland is likely to leave current club Borussia Dortmund in the summer should they fail to qualify for the Champions League.
The 20-year-old is attracting interest from clubs across Europe and it's a race to see who can seal a deal first.
Spanish publication AS claim Solskjaer 'keeps calling' and is eager to get Haaland on board with his project.
Solskjaer worked with Haaland while manager of Molde and knows firsthand how talented he is.
Lukaku joined Inter Milan in 2019 and since then United have used Anthony Martial and Edinson Cavani as their main striking options.
A move would see United dealing with Mino Raiola once again, despite his meddling in Paul Pogba's future.
Haaland has scored 33 goals in 31 games for Borussia Dortmund this season but the club are still four points off the Champions League places.
The latest strikes came in the form of a double in a 2-2 draw with Koln on Saturday and the result left Haaland furious.
European football expert Andy Brassell told talkSPORT: "Haaland scored a goal at the beginning and then again at the end of the game, and in between Koln held up their end of the bargain and were surprised to find just how bad Dortmund were, I think.
"Koln are really struggling at the back-end of the table and they were really close to getting a win thanks to a very uneven Dortmund performance.
"According to German tabloid reports Erling Haaland was very unhappy about this at the dressing room at half-time and insiders reported an outburst with numerous swears.
Haaland didn't look happy after the full time whistle :eyes: pic.twitter.com/xNz2mVrGLi- ESPN FC (@ESPNFC) March 20, 2021
"But the sulk at the end was something special.
"Jorge Mere, Koln's young Spanish defender, had asked for Haaland's shirt a couple of minutes before the end of the game, so as soon as the final whistle went Haaland takes off his shirt and thrusts it into the midwife of the waiting Mere, and Mere is stood there like, 'do you not want my shirt?'
"And 14 seconds after the final whistle went, Haaland is in the tunnel."
Featured Image Credit: PA Images
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