Hargreaves impressed on his City debut, scoring against Birmingham in the Carling Cup.
The 30-year-old - once an integral part of the international team under Sven-Goran Eriksson - was released by Manchester United following an injury-plagued spell.
However, Blues boss Roberto Mancini is in no doubt if Hargreaves stays fit, then an England recall ahead of the Euro 2012 finals should be on the agenda.
Marwood - who won the championship with Arsenal in 1989 and was also capped by England that season - believes it is now all about Hargreaves maintaining fitness levels.
"Everybody is delighted for Owen because it has been well documented the injury problems he has had over recent years," Marwood told BBC Radio Five Live's Sportsweek programme.
"He has worked hard to get back to the level of fitness at which he can compete in the Premier League.
"We are all hopeful he can stay healthy because he can make an enormous contribution not only to Manchester City, but potentially to the England national team."
Manchester United striker Michael Owen has accepted he is not part of Fabio Capello's England plans, but insists he will never turn his back on his country.
Marwood, 51, feels men with such experience as the former Liverpool and Real Madrid frontman can always offer something.
"Both Michael and Owen are quality players and they can still add an awful lot to the England squad," he said.
"But they need game and training time, if they do get that, then there is no reason why either of them should not force themselves back into the England squad."
Big-spending City moved level with United at the top of the Premier League yesterday after they beat Everton at Eastlands, and their rivals were held to a draw at Stoke.
While Marwood knows full well there is plenty more football to be played, everyone at City feels things are moving in the right direction.
"Anybody would want that sort of points return from the games we have played, but we are also realistic enough to know the season is still very early. There will be many twists and turns before we reach May," he said.
"We have definitely seen a progression of the team and the squad.
"It takes time for players to adapt, but we feel now the squad is very close and together, the performances have reflected that."