The Premier League pair have both been linked with the Borussia Dortmund superstar, who is said to be valued at around £150million.
Agent Mino Raiola and the player’s father Alf-Inge are on a tour of Europe, reportedly talking to potential suitors about a summer transfer.
Dortmund remain insistent they will keep the 20-year-old, but with a release clause set to come into effect in 2022, they could cash in this year.
And Scholes believes that United should target either Haaland or Harry Kane, with Ole Gunnar Solskjaer’s side still lacking a genuine No.9.
The Red Devils legend was speaking after his old side laboured to a 2-0 win over Granada in the first leg of their Europa League quarter final with Granada.
While Solskjaer’s men took full command of the tie, their lack of an archetypal centre forward was apparent against the physical Spaniards.
Asked what type of forward Solskjaer will target, he told BT Sport: “Haaland’s the obvious one, isn’t he? Harry Kane?
“These types of players, will they come to Manchester United at this point? Can United pay the money for them?
“I think they probably can, I think it’s up to them which club they choose. I think the two of them would probably have the choice of any club in Europe.”
If they are to sign Haaland, Old Trafford bosses will need to beat a number of the biggest clubs in Europe, but Scholes believes that between finances and need, Chelsea and United could be the last two standing.
When the former midfielder was pressed on whether United would spend big on him this year, he responded: “I think they probably would. If it meant getting Haaland, then why not?
“City don’t look like they want to pay. To be fair, with Guardiola, they very rarely play with a No.9 anyway, even when he’s had [Sergio] Aguero and [Gabriel] Jesus, he’s hardly played them.
“So is he the type of player Pep Guardiola wants? I’m not sure it is.
“It’s a player United will be desperate for, a player Chelsea will be desperate for.
“They’re probably the two clubs that would be able to afford to pay that fee.”
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