The Red Devils scored just 44 goals in the English Premier League this past season, ending in a lowly 15th place.
First-choice striker Rasmus Hojlund weighed in with just four league goals, while fellow frontmen Joshua Zirkzee and Alejandro Garnacho netted three and six goals respectively.
Osimhen bagged 26 goals as Galatasaray won the Turkish Super Lig, and Scholes feels the Nigerian hitman would be a welcome addition to their lacklustre strike force.
Scholes also called on United to consider a bid for Sporting's Swedish striker Viktor Gyokeres.
He said on The Overlap: "I think [Victor ] Osimhen, it sounds like a doable one.
"When you talk about financial problems, Osimhen could be doable. But I would keep [Rasmus] Hojlund.
"I know he is not been great, but he's a 22-year-old kid playing on his own for Manchester United the last two years.
"Manchester United should have at least three top centre forwards. I would have him and Osimhen. Him, Osimhen, and Gyokeres."
Man Utd have recently added to their ranks with the capture of Wolves attacker Matheus Cunha, who bagged 15 Premier League goals last term.
Manchester United have launched an ambitious move to sign Brentford's star forward Bryan Mbeumo, tabling a 55 million pounds offer that Brentford have rejected as too low, according to recent reports.
Manchester United winger Amad Diallo has been withdrawn from the Ivory Coast squad for two upcoming international friendlies in Canada.
Bruno Fernandes has confirmed that he has rejected a mega-money move to Saudi Arabian club Al Hilal to remain at Manchester United ahead of next season.
Jadon Sancho has confirmed his departure from Chelsea following the conclusion of his season-long loan, with the winger now expected to return to Manchester United amid uncertainty over his long-term future.
