Pulis claimed at a press conference that the Black Cats had tabled an offer of the 31-year-old Jamaica international.
However, Sunderland, who did make an enquiry earlier in the transfer window as they considered their options in the wake of Darren Bent's ?24million departure for Aston Villa, are adamant they have not made a bid.
Sources on Wearside described the claim, which is the latest in a series to have emerged from Staffordshire in the last week, as "nonsense".
Source: PA
Source: PA