The Cottagers have been linked with the England international in recent weeks and were thought to be preparing a bid.
However, manager martin Jol has ended his interest in the 19-year-old and looks set to make a move for Stekelenburg.
The Dutch international is reportedly free to leave the Serie A club after an 18-month spell for as little as £3m.
If they do press ahead with the move it would appear that their pursuit of Butland would come to an end.
Jol sees Stekelenburg as the ideal man to challenge Mark Schwarzer for the number one spot at the club, with current back-up David Stockdale failing to impress.
With the Australian stopper now 40-years-of-age, his playing time appears to be coming to an end, which will further tempt his manager into looking at other options.
Fulham were said to be highly interested in Butland, but their pursuit of other targets leaves Liverpool and Southampton as the front-runners for his signature.
It is believes that the Saints had a £6m bid rejected by the Championship club during the summer, but they are likely to accept a similar figure this month due to financial difficulties.
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