Hodgson believes time is still on Schwarzer's side. "Some of the best goalkeepers in the past have gone on to over 40," he said.
Schwarzer, who spent 11 years at Boro, said: "I'm enjoying myself more than ever, and I'm probably close to being as fit as I've ever been in my whole career.
"I want to keep going as long as I can. As long as I'm enjoying it, and able to play at this level, why not?"
Bobby Zamora's goals have made most of the headlines for Fulham this season but Schwarzer's consistency is a prime reason why the club could face Liverpool in next month's Europa League Final, just so long as they overcome Hamburg in a two-leg semi-final. Schwarzer said: "It's in our own hands. It would be a tremendous achievement for the players and club. We're all fighting for the same cause, we all want to be successful.
"We've got to stay focused and keep determined, and then the sky's the limit for us."
Indeed, if Fulham continue to defend as well as they did in Wolfsburg and at Liverpool, their season really could have a Cinderella finale.
Hodgson, who resisted the temptation to rest his leading lights, said: "After coming back from Wolfsburg with a clean sheet, and then coming to Anfield and getting another clean sheet, I've got to be very satisfied."
Zoltan Gera and Simon Davies were both missing through injury, but they could be back for the home game against Wolves on Saturday.