Haaland was Solskjaer’s top target during the January window, but the 19-year-old completed a move to Borussia Dortmund.
And despite claiming United’s front three of Marcus Rashford, Anthony Martial and Mason Greenwood could become a modern-day answer to Cristiano Ronaldo, Wayne Rooney and Carlos Tevez, Solskjaer remains intent on bolstering his attack.
Jadon Sancho remains high on the Norwegian’s summer wish-list, with the Dortmund winger capable of solving United’s long-standing problem position on the right.
Even without any additions, Solskjaer has transformed his forward line since succeeding Jose Mourinho.
Romelu Lukaku and Alexis Sanchez were shown the door, while Martial has been entrusted at the point of attack.
Rashford has become United’s talisman after finally being given a settled role on the left, while Greenwood’s promotion from the academy has been fast-tracked to spectacular effect.
Between them, the trio have outscored Liverpool’s feted forward line of Mo Salah, Sadio Mane and Roberto Firmino with a combined 39 goals, compared to 38.
Ahead of Sunday’s visit to Anfield, Solskjaer was happy to draw comparisons between both sides’ attacks.
He said: “The front three that they’ve got have been playing together for ages. Not ages but seasons now - and you can see the rotation, movements, understanding between them.
“We hope our front three will get that understanding in a while. I think I’ve only started them together once in the Premier League - the Newcastle game - so we’ve got a way to go to get the level of the three (at Liverpool), the understanding and consistency Liverpool have had - but they scored four goals in that game so it’s probably something I’ve got to look at more often.
“I believe in ours. We’re going to add to them as well, definitely, but in years coming I’m sure we’ll see lots of them.
“Liverpool have scored more goals than us, outside the front three, so I’m not going to say ours are better or theirs are better than ours.”
Solskjaer played in some devastating United attacks under Sir Alex Ferguson – most notably the treble-winning quartet which also included Dwight Yorke, Andy Cole and Teddy Sheringham.
But he looks to a different benchmark when assessing his current crop.
He added: “We’ve got them on long contracts, and we can see them developing into a very exciting front three.
“I was here with Ronaldo, Tevez, Rooney. That’s what we want as United supporters and manager . You want to see them express themselves, go to Anfield and put fear into their defenders.
“We’ve got Dan James here as well who adds to that so I’m very excited about it.”
Midfield is now Solskjaer’s priority this month, following injuries to Paul Pogba and Scott McTominay.
He is closing in on a deal for Bruno Fernandes – but he is only part way through his squad overhaul, which will wee Ashley Young become the latest player to depart when he completes a £1.3m move to Inter Milan.
United are hoping to put a dent in Liverpool’s procession towards their first league title in 30 years.
And Solskjaer insists the Merseysiders’ wait to return to the summit of English football cannot be repeated by United.
“That’s what we’re working hard to make sure doesn’t happen,” he said. “And let that be a lesson for us that we can’t let ourselves go another 24 years until we win the league and I’m sure we won’t.
“I believe in this club, I believe that we are rebuilding now, we’ve started something that’s going to take a little bit of time but we’ll get there.”