The 49-year-old feels his former charge would be able to handle the pressure of being a Red Devil if he wanted to leave Italy for England
Last summer, he swapped London for Turin, joining the Bianconeri on a free transfer, but has seen his game-time limited under former Chelsea boss Maurizio Sarri.
“I’ve been fortunate to see the best of Aaron when I was manager of Wales. He’s at his best when he’s under a bit of pressure, when he’s playing against the best teams and when he’s playing in the big games,” Coleman told the Mirror.
“If it’s not going to happen for him at Juventus, he’s definitely the type of player who can handle playing for Manchester United.
“When you play for a club like Manchester United the jersey is much heavier than when you are with a smaller club in the Premier League.
“If you play for a big club you’ve got to handle that extra weight. He certainly has the appetite for that.”
Coleman did not criticise Ramsey’s decision to move to Italy, but feels that the 29-year-old is too talented to not be a regular starter at club level.
The Welshman has played less than 800 minutes of league football for Juventus this season, scoring three goals and providing one assist in his time on the pitch.
“I understand why Aaron went to Juventus,” Coleman continued. “They are a great club and they always have a great chance of winning the league.
“He had been at Arsenal a long time, probably didn’t achieve what he wanted to achieve because Arsenal haven’t achieved what they would have liked in the last 10 years.