The Daily Star says the Trinidad & Tobago international is set to line up against Swansea City today, with the Welsh club already having had a £3m bid turned down.
Jones has scored four goals in eight games this season and came off the bench to net against Crystal Palace in the FA Cup.
But Potters boss Tony Pulis claims his in-demand striker has not reached the heights he did when he joined from Sunderland for £8m in 2010.
Pulis said: "I think Kenwyne's best spell was early on. That spell when he first joined he was absolutely outstanding.
"If there's going to be anything done we'll do our business with the football clubs. If we sell Kenwyne, I'll let you know. If we don't, I'll also let you know."