The Reds' midfielder, who only turned 18 earlier this month, is currently at a stand-off with the Anfield club over contract negotiations and the 68-year-old believes he would be the perfect replacement for Nani, should he be shown the exit door at Old Trafford.
It would be a sensational signing for United, who have enquired about the England international's availability, as the two clubs have not done business since Phil Chisnall's switch to Anfield way back in 1964.
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Morgan made 236 appearances for United from 1968 to 1975, scoring on 25 occasions and told the Manchester Evening News: "Sterling is the first winger I have seen in a long time who looks like a proper winger. He looks very good already and I think he is going to be great.
"If you just let him go wide on the outside of the full-backs all the time I think he will be a great player.
"He’ll frighten people to death, so long as nobody coaches it out of him. He’s the brightest prospect out there and would suit United."
Liverpool boss Brendan Rodgers is desperate to keep hold of his hottest prospect, who won his first senior cap in England's 4-2 defeat against Sweden last month.
Morgan believes signing Sterling would continue a long-standing tradition of quick wide men at Old Trafford, with George Best, Ryan Giggs and Cristiano Ronaldo going before him.
"It’s traditional United and is a great weapon," he added.
"Having two wingers going at a defence is exactly what opponents struggle to cope with these days.
"Full-backs generally are not good defenders any more. They are not equipped to deal with marking an out-and-out winger these days. They are half-baked forwards.
"Any side with wingers who can play are a winning team as far as I am concerned. It was good to see United use them at City and they really did stretch them."