Hart was dropped by City at the beginning of the month following a string of errors, with Manuel Pellegrini opting to give Costel Pantilimon a run in the first team.
However, Hart has retained the faith of England manager Roy Hodgson and is set to start Tuesday's friendly with Germany at Wembley.
Rosler, who earned five caps for East Germany, expects the 26-year-old to rise to the challenge.
"Joe has to understand he is accountable and his performance level has to step up, but he will do that – there is no question about it," Rosler told BBC Radio 5 Live.
"Joe Hart is undoubtedly the best goalkeeper in England and he has shown that in the past.
"Manchester City should be very privileged to have England's number one. I can't see anyone really challenging him.
"He has enough time now to get his form sorted before the World Cup and I think it is a great opportunity for him (against Germany) because he will be tested."
Rosler believes Germany will be under significant pressure in Brazil next summer as they bid to claim a first major title in 18 years.
He added: "Germany normally does very well in big tournaments. They've had a lot of praise for how they have played in the last few years and everyone in Germany is ready for a title.
"I think the pressure is on for the 2014 World Cup, even more than the previous ones because Germany have come very close, but haven't won anything since 1996 (when they claimed the European Championship)."
