The 29-year-old has been linked with a move away from Roma in recent months.
Stekelenburg only joined the Italian giants from Dutch side Ajax last summer.
But Fulham are confident of signing the goalkeeper, who has previously been linked with the likes of Manchester United and Arsenal.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.