Sunderland are looking for a striker to replace Darren Bent, who moved to Aston Villa for an initial £18m on Tuesday.
Meanwhile, goalkeeper Carlo Nash, 37, has signed a one-year contract extension at the Britannia Stadium.
Fuller, who has been Stoke's leading goalscorer in each of the last three seasons, has found the net three times so far this campaign.
More to follow.
Source: BBC Sport
Source: BBC Sport