The Dutch international has not been first choice throughout this season at Roma, losing out to Uruguayan Mauro Goicoechea under Zdenek Zeman.
Reports had claimed that Martin Jol was ready to turn his attention to Stekelenburg as the long-term successor to Mark Schwarzer.
However, his representative Rob Jansen has denied any talks have taken place and he has had no contact with Fulham.
"I indeed categorically deny these rumours, there has been no contact with the London club or with their manager Martin Jol," Jansen told Calciomercato.
"He is happy in Roma and he wants to stay there - his relationship with Zeman is excellent."
Stekelenburg, who was considered by Sir Alex Ferguson at Manchester United before he signed David de Gea, joined Roma from Ajax in the summer of 2011.
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