It was reported on Thursday that the Dutch stopper had received an offer from the Cottagers but as he was due to depart for London to discuss personal terms, he was informed by his agent that Roma had decided to keep him at the club for the remainder of the season.
Stekelenburg told sportpromotion.nl: "This feels like a major setback in many ways. I was really looking forward to getting started at Fulham.
"It is a great club and it would be an understatement to say the league is great too. It is a blow and I will need time to process it."
The 30-year-old has failed to hold down a regular place in Roma's starting lineup since he joined the club from Ajax in 2011.