The Holland international has been strongly linked with a move to England, with Fulham and Arsenal said to be keen.
The Cottagers were believed to be leading the chase, with David Stockdale having headed out of the club on loan and hinting at making a permanent switch to Hull City.
Stekenlenburg, who has been capped on 54 occasions by his country, was considered to be an ideal replacement, as he would bring considerable experience to England.
His representative has, however, revealed that no official offers have been received as yet.
Rob Jansen told calciomercato.it: "At the moment there are just rumours and speculation.
"We have yet to receive a concrete offer, so it is therefore probable that he will stay at Roma in January rather than leave.
"We know what is moving in the goalkeeping market, but nothing has been decided."