The 31-year-old was first-choice for the Netherlands at the 2012 European Championship and also started the 2010 World Cup final in South Africa.
However, he has since dropped down the pecking order for his national side and a move to the Premier League did little to revive his fortunes.
Stekelenburg suffered a shoulder injury on his debut for Fulham and things went from bad to worse as the club were eventually relegated, with David Stockdale preferred in goal towards the end of the campaign.
Having lost out to Jasper Cillessen, Michel Vorm and Tim Krul for a place in the Netherlands' World Cup squad, Stekelenburg has taken responsibility for his downturn in fortunes.
"I think you always have to blame yourself first," he told De Telegraaf. "If I had played at the high level I did in 2010 there would be no reason for the coach (Louis van Gaal) to overlook me.
"I came to Fulham to keep the club in the Premier League and to fight to get myself in the World Cup squad. I failed on both counts."
With the prospect of Championship football looming next season, Stekelenburg is hoping to secure a move away from Fulham and believes he can still perform at the highest level.
"I'm 31, very fit and want to get back to playing," he added. "On the 25th I report back to Fulham because I am still under contract there for three years.
"And then we'll see. My agent is working hard to find a satisfactory solution for everyone.
"I can't wait to get back to the Maarten Stekelenburg of 2010, but with more experience."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.