It has been reported that the Quins skipper could be stripped of the armband by national team coach Stuart Lancaster, with Northampton Saints' flanker Tom Wood the favourite to lead the side.
However, O'Shea believes that Robshaw is still the right man to captain his country for the matches against Australia, Argentina and New Zealand.
"It's Stuart's call but he's a magnificent leader and leads by example," he told Sky Sports News. "What he's achieved over the last couple of years and what he's given to England and Harlequins is very hard to second guess.
"He'll be desperate to get back into the England team, desperate to have the England captaincy.
"It's Stuart's call but I'd have him as my captain every day of the week. He's started the season in good form and hopefully he'll prove that this week."
England welcome Australia to Twickenham Stadium on November 2.