Zakuani, who first joined the Potters in January 2007, spent the remainder of last season at the Britannia.
He rejoined City for a second loan spell in August and will remain with Stoke until the end of the season.
"The best thing for me to do is to wait and see how the season pans out," said the DR Congo international. "I'm happy here, but I'm also happy at Fulham so it's not a bad choice to be making.
"There's a few things for me to discuss, like how much they value me and how much I want to move, but basically I will be taking the best offer that comes along."
Any deal may yet be affected by the two sides' respective league positions come May.
As things stand, Stoke could be playing Premier League football next season. And, to add a significant touch of irony, they could well swap places along the way with Zakuani's parent club Fulham, who are 19th in the top flight and one of the bookies' leading favourites to go down.
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