City won the Premier League title last season on the final day on goal difference, with United finishing second.
The Citizens have been linked with a number of players this summer with Arsenal striker Robin van Persie their main target, and are widely said to possess the best and most extensive squad in England.
Marsh, 67, is delighted with his former club's growth in stature and is confident that they are on to achieving more success ahead.
"I think City are on the way to the absolute top of football – while United are on the way down," he is quoted as saying in the Daily Star.
"City will be the team who win the trophies over the next few years."
City will begin the defence of their Premier League title with a home game against Southampton on Sunday, August 19, while United will kick off their campaign against Everton away the following day.